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MSCE Physics practice questions

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Question 1Scientific Inquiry, Measurement, and the Nature of Physics

A student measures the length of a metal rod five times and obtains 12.51 cm, 12.49 cm, 12.50 cm, 12.52 cm, and 12.50 cm. The accepted value is 12.70 cm. Which statement best describes the student's measurements?

  1. They are neither accurate nor precise.
  2. They are both accurate and precise.
  3. They are precise but not accurate. Correct answer.
  4. They are accurate but not precise.

Explanation

Precision refers to how closely repeated measurements agree with each other, while accuracy refers to how close a measurement is to the accepted value. The five readings cluster tightly within 0.03 cm, so they are precise, but they all differ from 12.70 cm by about 0.2 cm, so they are not accurate. Systematic error, such as a zero error in the instrument, commonly produces this pattern.

Question 2Scientific Inquiry, Measurement, and the Nature of Physics

Which of the following is a base SI unit?

  1. joule
  2. pascal
  3. newton
  4. kilogram Correct answer.

Explanation

The SI system defines seven base units from which all others are derived, and the kilogram is the base unit of mass. The newton, joule, and pascal are all derived units built from combinations of base units. For example, one newton equals one kilogram metre per second squared.

Question 3Scientific Inquiry, Measurement, and the Nature of Physics

A student records the mass of a sample as 0.004560 kg. How many significant figures does this value have?

  1. Four Correct answer.
  2. Three
  3. Five
  4. Seven

Explanation

Leading zeros that merely place the decimal point are never significant, so the three zeros before the 4 are ignored. The digits 4, 5, 6, and the trailing zero after the 6 are all significant because the trailing zero follows a decimal digit. This gives four significant figures.

Question 4Scientific Inquiry, Measurement, and the Nature of Physics

Which statement best describes the role of a hypothesis in scientific inquiry?

  1. It is a testable proposed explanation that can be supported or refuted by evidence. Correct answer.
  2. It is a personal opinion that requires no evidence.
  3. It is a proven law that cannot be revised.
  4. It is the final conclusion reached after all experiments.

Explanation

A hypothesis is a proposed, testable explanation for an observation, framed so that predictions can be checked against evidence. It is provisional: experiments can support it or refute it, and it may be revised. This provisional, testable character is central to how physics builds knowledge.

Question 5Scientific Inquiry, Measurement, and the Nature of Physics

In an experiment, a student plots values of a dependent variable against an independent variable and draws a line of best fit. What is the main purpose of this line?

  1. To eliminate the need to record uncertainties
  2. To reveal the underlying trend and allow interpolation between data points Correct answer.
  3. To identify which variable is the independent variable
  4. To pass through every plotted data point exactly

Explanation

A line of best fit summarises the overall trend in scattered data, averaging out random variation. It allows values to be interpolated between measured points and the relationship to be characterised mathematically. It does not need to pass through every point, since real data contain random scatter.

Question 6Scientific Inquiry, Measurement, and the Nature of Physics

A quantity is reported as 25.0 ± 0.5 m. What does the ±0.5 m represent?

  1. The range of values the true value could never take
  2. The absolute uncertainty in the measurement Correct answer.
  3. The random error only, excluding systematic error
  4. The percentage uncertainty in the measurement

Explanation

The ± value states the absolute uncertainty, the estimated margin within which the true value is expected to lie. It is expressed in the same unit as the measurement itself. Percentage uncertainty would instead be 0.5/25.0 × 100%, which is 2%.

Question 7Scientific Inquiry, Measurement, and the Nature of Physics

A student measures the diameter of a wire with a micrometer screw gauge that has a zero error of −0.02 mm. The reading on the instrument is 1.48 mm. What is the corrected diameter?

  1. 1.46 mm
  2. 1.50 mm Correct answer.
  3. 1.48 mm
  4. 1.44 mm

Explanation

A negative zero error means the instrument reads below zero when closed, so every reading is too small by 0.02 mm. The correction is therefore to add 0.02 mm to the observed reading. This gives 1.48 + 0.02 = 1.50 mm.

Question 8Scientific Inquiry, Measurement, and the Nature of Physics

A rectangular plate has measured dimensions 4.0 cm × 6.0 cm, each to two significant figures. What is the area expressed to the appropriate number of significant figures?

  1. 24.0 cm²
  2. 2.4 × 10¹ cm²
  3. 20 cm²
  4. 24 cm² Correct answer.

Explanation

When multiplying measured quantities, the result should carry the same number of significant figures as the input with the fewest. Both inputs have two significant figures, so the area must be given to two significant figures. The product is 24 cm², already two significant figures.

Question 9Scientific Inquiry, Measurement, and the Nature of Physics

A student measures the period of a pendulum as 2.0 s with an absolute uncertainty of 0.1 s. What is the percentage uncertainty in the period?

  1. 20%
  2. 0.05%
  3. 10%
  4. 5% Correct answer.

Explanation

Percentage uncertainty equals the absolute uncertainty divided by the measured value, multiplied by 100. Here that is (0.1/2.0) × 100 = 5%. Percentage uncertainty is dimensionless and allows comparison of precision across measurements of different sizes.

Question 10Scientific Inquiry, Measurement, and the Nature of Physics

Which of the following combinations of quantities has the same SI base-unit dimensions as power?

  1. Force × velocity Correct answer.
  2. Mass × acceleration
  3. Force × distance
  4. Energy ÷ distance

Explanation

Power is the rate of doing work, so its dimensions are energy per unit time, or kg·m²·s⁻³. Force × velocity gives kg·m·s⁻² multiplied by m·s⁻¹, which equals kg·m²·s⁻³, matching power. Dimensional analysis like this is a routine check on derived equations.

Question 11Scientific Inquiry, Measurement, and the Nature of Physics

A student writes a length as 0.00320 m. Which representation correctly expresses this in scientific notation with the same number of significant figures?

  1. 3.2 × 10⁻³ m
  2. 0.320 × 10⁻² m
  3. 3.20 × 10⁻³ m Correct answer.
  4. 32.0 × 10⁻⁴ m

Explanation

Scientific notation places one non-zero digit before the decimal point and preserves significant figures in the mantissa. The value 0.00320 m has three significant figures, so the mantissa must be 3.20. Moving the decimal three places gives 3.20 × 10⁻³ m.

Question 12Scientific Inquiry, Measurement, and the Nature of Physics

In an investigation, a student changes the load on a spring and measures its extension, keeping the spring and the measuring method the same. Which variable is the independent variable?

  1. The extension of the spring
  2. The stiffness of the spring
  3. The length of the ruler used
  4. The load applied to the spring Correct answer.

Explanation

The independent variable is the one deliberately changed by the investigator, and here the student varies the load. The extension is the dependent variable because it responds to the load. Controlled variables, such as the spring itself and the measuring method, are held constant.

Question 13Scientific Inquiry, Measurement, and the Nature of Physics

A set of repeated timings gives a mean of 4.62 s with a spread of ±0.08 s. Another set gives a mean of 4.60 s with a spread of ±0.02 s. What is the most defensible comparison of the two results?

  1. Reliability cannot be compared from these data.
  2. The second set is more reliable because its spread is smaller. Correct answer.
  3. The two sets are equally reliable because their means are similar.
  4. The first set is more reliable because its mean is larger.

Explanation

Reliability improves when repeated readings cluster closely, which is reflected in a smaller spread or uncertainty. The second set has a spread of ±0.02 s against ±0.08 s, so it is more reliable. The size of the mean itself says nothing about reliability.

Question 14Scientific Inquiry, Measurement, and the Nature of Physics

A student claims that an experiment has produced a result that is inconsistent with the accepted value. Which action is most appropriate as a next step in scientific inquiry?

  1. Assume the accepted value is wrong and publish immediately
  2. Discard the result without recording it
  3. Repeat the measurement and examine possible systematic errors Correct answer.
  4. Adjust the data so the result matches the accepted value

Explanation

Scientific inquiry requires that anomalous results be investigated rather than hidden or fabricated. Repeating measurements and checking for systematic errors, such as calibration faults, tests whether the discrepancy is real. Only after such checks can a genuine challenge to an accepted value be justified.

Question 15Scientific Inquiry, Measurement, and the Nature of Physics

The equation for the period of a simple pendulum is T = 2π√(L/g). Which statement correctly describes how the period depends on the length L, according to this relationship?

  1. T is independent of L.
  2. T is directly proportional to L.
  3. T is directly proportional to √L. Correct answer.
  4. T is inversely proportional to L.

Explanation

In the equation T = 2π√(L/g), the period is proportional to the square root of the length. Doubling L therefore increases T by a factor of √2, not by a factor of two. This is why a graph of T against √L is a straight line through the origin.

Question 16Scientific Inquiry, Measurement, and the Nature of Physics

Which of the following best explains why physicists use models rather than direct observation of every phenomenon?

  1. Models are only used when mathematics cannot be applied.
  2. Models simplify complex systems so that key relationships can be analysed and predicted. Correct answer.
  3. Models replace the need for experimental evidence.
  4. Models are exact copies of reality that remove all uncertainty.

Explanation

Models deliberately simplify a system by retaining the features relevant to the question and ignoring others. This makes complex phenomena tractable and allows predictions that can be tested experimentally. A model is judged by how well its predictions match observation, not by being a perfect copy of reality.

Question 17Scientific Inquiry, Measurement, and the Nature of Physics

A student uses a stopwatch to time 20 oscillations of a pendulum and divides the total time by 20. Which statement best explains why this improves the measurement?

  1. It makes the period independent of the pendulum length.
  2. It reduces the random timing uncertainty per oscillation. Correct answer.
  3. It increases the number of significant figures in the stopwatch reading.
  4. It removes any systematic error in the stopwatch.

Explanation

Reaction-time error in starting and stopping the stopwatch is roughly constant for each timing, so it becomes a smaller fraction of a longer total interval. Dividing the total by the number of oscillations therefore reduces the random uncertainty per oscillation. Systematic errors, such as a stopwatch running slow, are not removed by this method.

Question 18Scientific Inquiry, Measurement, and the Nature of Physics

A quantity Q is calculated from measurements as Q = a²b/c. The percentage uncertainties in a, b, and c are 2%, 3%, and 4% respectively. What is the percentage uncertainty in Q?

  1. 13%
  2. 11% Correct answer.
  3. 5%
  4. 9%

Explanation

For a product or quotient, percentage uncertainties add. A power raises the percentage uncertainty by that power, so a² contributes 2 × 2% = 4%. Adding the contributions gives 4% + 3% + 4% = 11%.

Question 19Scientific Inquiry, Measurement, and the Nature of Physics

A graph of the square of the period T² against the length L of a simple pendulum gives a straight line through the origin with gradient m. Given that T² = (4π²/g)L, what does the gradient m allow the student to determine?

  1. The amplitude of the oscillations
  2. The mass of the pendulum bob
  3. The length of the pendulum at rest
  4. The acceleration of free fall g Correct answer.

Explanation

Comparing T² = (4π²/g)L with y = mx shows that the gradient m equals 4π²/g. Rearranging gives g = 4π²/m, so the gradient yields the acceleration of free fall. Linearising the relationship in this way is a standard experimental technique.

Question 20Scientific Inquiry, Measurement, and the Nature of Physics

A measurement is quoted as 9.80 m s⁻² for g, with an uncertainty of 0.05 m s⁻². Which statement correctly interprets this result?

  1. The true value lies exactly at 9.80 m s⁻².
  2. The measurement has a percentage uncertainty of 0.5%.
  3. The uncertainty is negligible because it is small compared with 9.80.
  4. The true value is expected to lie between about 9.75 and 9.85 m s⁻². Correct answer.

Explanation

An absolute uncertainty of ±0.05 m s⁻² defines a range around the measured value within which the true value is expected to lie. Adding and subtracting the uncertainty gives 9.75 to 9.85 m s⁻². The percentage uncertainty is 0.05/9.80 × 100 ≈ 0.51%, not 0.5% exactly.

Question 21Mechanics: Kinematics and Dynamics

A car starts from rest and accelerates uniformly at 2.5 m/s² for 8.0 s. How far does it travel during this interval?

  1. 40 m
  2. 80 m Correct answer.
  3. 160 m
  4. 20 m

Explanation

With zero initial velocity, displacement is s = ½at². Substituting a = 2.5 m/s² and t = 8.0 s gives ½ × 2.5 × 64 = 80 m. The result scales with the square of time, so doubling the time quadruples the distance.

Question 22Mechanics: Kinematics and Dynamics

Which quantity is a vector, requiring both magnitude and direction to be fully specified?

  1. Time
  2. Speed
  3. Distance
  4. Displacement Correct answer.

Explanation

Displacement is the straight-line change in position from start to finish, so it carries a direction as well as a magnitude. Speed, distance and time are scalars, fully described by a number with units.

Question 23Mechanics: Kinematics and Dynamics

A ball is thrown vertically upward with an initial speed of 20 m/s. Taking g = 10 m/s² and ignoring air resistance, what is the maximum height reached above the release point?

  1. 20 m Correct answer.
  2. 10 m
  3. 30 m
  4. 40 m

Explanation

At maximum height the vertical velocity is zero, so v² = u² − 2gh gives 0 = 400 − 20h. Solving yields h = 20 m. The mass of the ball does not appear, because gravitational acceleration is independent of mass.

Question 24Mechanics: Kinematics and Dynamics

According to Newton's first law, a body continues in its state of rest or uniform motion in a straight line unless acted on by

  1. a frictional torque
  2. a change in mass
  3. any internal force
  4. a net external force Correct answer.

Explanation

Newton's first law states that a resultant (net) external force is required to change a body's translational state of motion. Balanced forces cancel, so the body remains at rest or moves uniformly. Internal forces within a system cannot change the motion of its centre of mass.

Question 25Mechanics: Kinematics and Dynamics

A 4.0 kg block rests on a horizontal surface where the coefficient of static friction is 0.30. Taking g = 10 m/s², what is the minimum horizontal force needed to just start the block moving?

  1. 4.0 N
  2. 40 N
  3. 12 N Correct answer.
  4. 1.2 N

Explanation

On a horizontal surface the normal force equals the weight, N = mg = 40 N. The limiting static friction is f = μsN = 0.30 × 40 = 12 N, so a slightly larger applied force is needed to initiate motion. The coefficient multiplies the normal force, not the mass.

Question 26Mechanics: Kinematics and Dynamics

A cyclist covers 150 m in 25 s at constant speed. What is the cyclist's speed?

  1. 3.0 m/s
  2. 9.0 m/s
  3. 12 m/s
  4. 6.0 m/s Correct answer.

Explanation

For constant speed, v = distance ÷ time. Dividing 150 m by 25 s gives 6.0 m/s. Constant speed means the average and instantaneous values are identical here.

Question 27Mechanics: Kinematics and Dynamics

Which statement correctly describes the acceleration of a projectile moving freely under gravity alone near Earth's surface?

  1. It increases as the projectile falls toward the ground.
  2. It is constant in magnitude and direction throughout the flight. Correct answer.
  3. It is zero at the highest point of the trajectory.
  4. It points along the direction of instantaneous velocity.

Explanation

Ignoring air resistance, the only force on a projectile is its weight, so the acceleration is g directed vertically downward at every instant. This holds at the apex too, where velocity is horizontal but acceleration is still g. The acceleration does not depend on speed or height.

Question 28Mechanics: Kinematics and Dynamics

A force of 30 N acts on a 6.0 kg object on a frictionless surface. What is the resulting acceleration?

  1. 0.20 m/s²
  2. 180 m/s²
  3. 5.0 m/s² Correct answer.
  4. 2.0 m/s²

Explanation

Newton's second law gives a = F/m. Dividing 30 N by 6.0 kg yields 5.0 m/s². The units confirm this: one newton is one kilogram-metre per second squared.

Question 29Mechanics: Kinematics and Dynamics

A block slides down a rough incline at constant velocity. Which statement about the forces on the block is correct?

  1. The net force on the block points down the incline.
  2. The normal force equals the full weight of the block.
  3. Kinetic friction acts down the incline alongside the weight component.
  4. The component of weight along the incline equals the kinetic friction force. Correct answer.

Explanation

Constant velocity means zero acceleration, so the net force along the incline must be zero. The downslope weight component is therefore balanced by the upslope kinetic friction. The normal force equals the perpendicular weight component, mg cosθ, which is less than the full weight.

Question 30Mechanics: Kinematics and Dynamics

A ball is projected horizontally at 15 m/s from a cliff 45 m high. Taking g = 10 m/s², how far from the base of the cliff does it land?

  1. 30 m
  2. 45 m Correct answer.
  3. 60 m
  4. 15 m

Explanation

Horizontal and vertical motions are independent. The fall time follows from 45 = ½ × 10 × t², giving t = 3.0 s. In that time the horizontal range is 15 × 3.0 = 45 m, since horizontal velocity stays constant.

Question 31Mechanics: Kinematics and Dynamics

A 1200 kg car travelling at 20 m/s brakes to rest in 5.0 s. What is the magnitude of the average braking force?

  1. 2400 N
  2. 4800 N Correct answer.
  3. 9600 N
  4. 24000 N

Explanation

The average acceleration has magnitude a = Δv/Δt = 20/5.0 = 4.0 m/s². Newton's second law then gives F = ma = 1200 × 4.0 = 4800 N. The force acts opposite the direction of motion.

Question 32Mechanics: Kinematics and Dynamics

A person of mass 60 kg stands in a lift that accelerates upward at 2.0 m/s². Taking g = 10 m/s², what is the normal force exerted by the floor on the person?

  1. 1200 N
  2. 480 N
  3. 720 N Correct answer.
  4. 600 N

Explanation

Taking upward as positive, N − mg = ma, so N = m(g + a) = 60 × (10 + 2.0) = 720 N. The floor must push harder than the weight to provide the upward acceleration. In a lift accelerating downward the apparent weight would be smaller than mg.

Question 33Mechanics: Kinematics and Dynamics

Two blocks of masses 3.0 kg and 5.0 kg are pushed together across a frictionless floor by a 16 N horizontal force applied to the 3.0 kg block. What is the magnitude of the contact force between the blocks?

  1. 8.0 N
  2. 10 N Correct answer.
  3. 16 N
  4. 6.0 N

Explanation

The whole system accelerates at a = 16/8.0 = 2.0 m/s². The contact force is the only horizontal force on the 5.0 kg block, so it equals 5.0 × 2.0 = 10 N. The 3.0 kg block experiences 16 N forward and 10 N backward, giving the same acceleration.

Question 34Mechanics: Kinematics and Dynamics

A car's velocity–time graph is a straight line rising from 5 m/s at t = 0 to 25 m/s at t = 10 s. What is the displacement over this interval?

  1. 100 m
  2. 150 m Correct answer.
  3. 250 m
  4. 200 m

Explanation

Displacement is the area under the velocity–time graph, a trapezium here. The area is ½ × (5 + 25) × 10 = 150 m. The same result follows from s = ut + ½at² with a = 2.0 m/s².

Question 35Mechanics: Kinematics and Dynamics

A skydiver reaches terminal velocity. Which statement best explains this condition?

  1. The drag force and weight act in the same direction and add.
  2. The weight becomes zero once the skydiver is falling fast enough.
  3. The drag force exceeds the weight, so the skydiver decelerates.
  4. The drag force equals the weight, so the net force is zero. Correct answer.

Explanation

Terminal velocity occurs when the upward drag force grows with speed until it balances the downward weight. With zero net force, acceleration is zero and the skydiver falls at constant speed. The weight does not vanish; it is simply balanced.

Question 36Mechanics: Kinematics and Dynamics

A 2.0 kg ball moving at 6.0 m/s collides head-on with a stationary 4.0 kg ball. After the collision the 2.0 kg ball moves at 2.0 m/s in the same direction. What is the velocity of the 4.0 kg ball?

  1. 4.0 m/s in the original direction
  2. 2.0 m/s in the original direction Correct answer.
  3. 2.0 m/s opposite the original direction
  4. 1.0 m/s in the original direction

Explanation

Momentum is conserved: 2.0 × 6.0 = 2.0 × 2.0 + 4.0 × v. This gives 12 = 4 + 4v, so v = 2.0 m/s in the original direction. The value is positive, so the heavier ball moves forward.

Question 37Mechanics: Kinematics and Dynamics

A 0.50 kg ball hits a wall horizontally at 8.0 m/s and rebounds at 6.0 m/s. If the contact time is 0.10 s, what is the magnitude of the average force on the ball?

  1. 10 N
  2. 40 N
  3. 70 N Correct answer.
  4. 140 N

Explanation

Taking the initial direction as positive, the change in momentum is Δp = m(v_f − v_i) = 0.50 × (−6.0 − 8.0) = −7.0 kg·m/s. The average force magnitude is |Δp|/Δt = 7.0/0.10 = 70 N. The rebound reverses the velocity sign, so the speeds add rather than subtract.

Question 38Mechanics: Kinematics and Dynamics

A projectile is launched at 30 m/s at 40° above the horizontal on level ground, with g = 10 m/s². Which quantity is unchanged throughout the flight (ignoring air resistance)?

  1. The vertical component of velocity
  2. The magnitude of the velocity
  3. The direction of the velocity
  4. The horizontal component of velocity Correct answer.

Explanation

No horizontal force acts on the projectile, so its horizontal velocity component v cosθ remains constant. The vertical component changes because gravity acts downward, which also changes the speed and direction continuously.

Question 39Mechanics: Kinematics and Dynamics

A 5.0 kg crate is pulled at constant speed across a rough horizontal floor by a horizontal rope with tension 20 N. What is the coefficient of kinetic friction?

  1. 2.5
  2. 0.40 Correct answer.
  3. 0.50
  4. 0.20

Explanation

Constant speed means the tension balances kinetic friction, so f = 20 N. The normal force equals the weight, mg = 50 N. Thus μk = f/N = 20/50 = 0.40.

Question 40Mechanics: Kinematics and Dynamics

A ball is thrown horizontally from a table and a second identical ball is dropped from rest at the same instant from the same height. Ignoring air resistance, which statement is true?

  1. Both balls land at the same time because vertical motion is independent of horizontal motion. Correct answer.
  2. The thrown ball lands first because its greater speed reduces the fall time.
  3. The dropped ball lands first because it has no horizontal motion.
  4. The thrown ball lands later because it travels farther.

Explanation

Both balls start with zero vertical velocity and fall the same height under gravity, so their vertical motions are identical. The horizontal velocity of the thrown ball does not affect its fall time. This independence of perpendicular components is the basis of projectile analysis.

Question 41Mechanics: Kinematics and Dynamics

A particle moves in a straight line with velocity given by v = 3t² − 12t (SI units). At what time is its acceleration zero?

  1. t = 4.0 s
  2. t = 2.0 s Correct answer.
  3. t = 6.0 s
  4. t = 1.0 s

Explanation

Acceleration is the time derivative of velocity, a = dv/dt = 6t − 12. Setting this to zero gives t = 2.0 s. At that instant the velocity is momentarily at a minimum, not zero, since v(2) = −12 m/s.

Question 42Mechanics: Kinematics and Dynamics

A 3.0 kg block on a frictionless table is connected by a light string over a frictionless pulley to a hanging 2.0 kg mass. Taking g = 10 m/s², what is the acceleration of the system?

  1. 5.0 m/s²
  2. 10 m/s²
  3. 4.0 m/s² Correct answer.
  4. 2.0 m/s²

Explanation

The net driving force is the hanging weight, 20 N, and the total mass accelerated is 5.0 kg. Thus a = 20/5.0 = 4.0 m/s². Using only the hanging mass would wrongly give g.

Question 43Mechanics: Kinematics and Dynamics

A ball is thrown vertically upward and returns to the thrower's hand. Taking upward as positive and ignoring air resistance, which description of its acceleration is correct?

  1. Negative on the way up and positive on the way down
  2. Negative throughout the flight Correct answer.
  3. Positive on the way up and negative on the way down
  4. Zero at the apex and negative elsewhere

Explanation

Gravity acts downward at all times, so with upward positive the acceleration is −g throughout, including at the apex. Only the velocity changes sign as the ball reverses direction. A common error is to assume acceleration follows the direction of motion.

Question 44Mechanics: Kinematics and Dynamics

A block of mass m rests on a rough incline of angle θ and is on the point of sliding. If the angle is increased slightly, the block accelerates. Which expression gives the coefficient of static friction at the threshold of sliding?

  1. cos θ
  2. 1/cos θ
  3. tan θ Correct answer.
  4. sin θ

Explanation

At the threshold, the downslope weight component mg sinθ just equals the limiting friction μs mg cosθ. Cancelling mg and rearranging gives μs = tanθ. This explains why the angle of repose depends only on the friction coefficient.

Question 45Mechanics: Kinematics and Dynamics

Two forces act on a particle: 6.0 N due east and 8.0 N due north. What is the magnitude of the resultant force?

  1. 2.0 N
  2. 7.0 N
  3. 10 N Correct answer.
  4. 14 N

Explanation

Perpendicular forces combine by the Pythagorean theorem: R = √(6.0² + 8.0²) = √100 = 10 N. The resultant points at about 53° north of east. Simple addition would only apply if the forces were parallel.

Question 46Mechanics: Kinematics and Dynamics

A particle moves along the x-axis with its position given by x = 2t³ − 9t² + 12t + 5, where x is in metres and t is in seconds. At which time is the particle momentarily at rest?

  1. t = 3.0 s
  2. t = 2.0 s
  3. t = 1.5 s
  4. t = 1.0 s Correct answer.

Explanation

Velocity is the derivative of position: v = dx/dt = 6t² − 18t + 12. Setting v = 0 gives t² − 3t + 2 = 0, so t = 1 s or t = 2 s. The particle is momentarily at rest at both times, but only t = 1.0 s is listed among the options.

Question 47Mechanics: Kinematics and Dynamics

A ball is thrown vertically upward with an initial speed of 20 m/s from the edge of a cliff 60 m high. Taking upward as positive and g = 10 m/s², how long does it take for the ball to reach the ground below?

  1. 8.0 s
  2. 6.0 s Correct answer.
  3. 2.0 s
  4. 4.0 s

Explanation

Use y = v₀t − ½gt² with y = −60 m (ground below launch) and v₀ = +20 m/s. This gives −60 = 20t − 5t², or t² − 4t − 12 = 0, which factors as (t − 6)(t + 2) = 0. The positive root is t = 6.0 s.

Question 48Mechanics: Kinematics and Dynamics

A block of mass 2.0 kg is pulled along a rough horizontal surface by a horizontal force of 10 N. The coefficient of kinetic friction between the block and the surface is 0.25. Taking g = 10 m/s², what is the acceleration of the block?

  1. 0 m/s²
  2. 7.5 m/s²
  3. 2.5 m/s² Correct answer.
  4. 5.0 m/s²

Explanation

The normal force is N = mg = 20 N, so kinetic friction is f = μN = 0.25 × 20 = 5 N. The net horizontal force is 10 − 5 = 5 N, giving a = F_net/m = 5/2.0 = 2.5 m/s².

Question 49Mechanics: Kinematics and Dynamics

A car accelerates uniformly from rest and covers 100 m in 10 s. What is its acceleration?

  1. 10 m/s²
  2. 2.0 m/s² Correct answer.
  3. 5.0 m/s²
  4. 1.0 m/s²

Explanation

Using s = ut + ½at² with u = 0, we get 100 = ½ a (10)² = 50a, so a = 2.0 m/s².

Question 50Mechanics: Kinematics and Dynamics

A 5.0 kg object is subjected to two forces: 10 N to the right and 4.0 N to the left. What is the acceleration of the object?

  1. 1.2 m/s² to the right Correct answer.
  2. 2.8 m/s² to the right
  3. 2.0 m/s² to the right
  4. 0.8 m/s² to the right

Explanation

The net force is 10 − 4 = 6 N to the right. By Newton's second law, a = F_net/m = 6/5.0 = 1.2 m/s² to the right.