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Question 1Kinematics
A runner moves along a straight track. Which quantity is a vector?
- Displacement Correct answer.
- Average speed
- Distance traveled
- Elapsed time
Explanation
Displacement is the change in position and includes both magnitude and direction, so it is a vector. Speed, distance, and time are scalars with magnitude only.
Question 2Kinematics
A cyclist rides 300 m east, then turns and rides 100 m west. What is the magnitude of the cyclist's displacement?
- 200 m Correct answer.
- 300 m
- 100 m
- 400 m
Explanation
Displacement depends only on the change in position, not the total path. Taking east as positive gives 300 m - 100 m = 200 m.
Question 3Kinematics
An object moves in a straight line with constant velocity. What is true of its acceleration?
- It is zero Correct answer.
- It is opposite to the velocity
- It is constant and nonzero
- It increases steadily
Explanation
Acceleration is the rate of change of velocity. If the velocity is constant, its rate of change is zero, so the acceleration is zero.
Question 4Kinematics
A car travels 150 m in 10 s at constant speed. What is its speed?
- 15 m/s Correct answer.
- 1.5 m/s
- 0.067 m/s
- 150 m/s
Explanation
For constant speed, speed equals distance divided by time. Dividing 150 m by 10 s gives 15 m/s.
Question 5Kinematics
In a position-versus-time graph for a moving object, what does the slope of the line represent?
- Velocity Correct answer.
- Acceleration
- Distance traveled
- Displacement
Explanation
The slope of a position-versus-time graph is the change in position divided by the change in time, which is velocity. Acceleration corresponds to the slope of a velocity-versus-time graph.
Question 6Kinematics
A ball is dropped from rest and falls freely near Earth's surface. What is its speed after 3.0 s, taking g = 10 m/s²?
- 30 m/s Correct answer.
- 3.0 m/s
- 10 m/s
- 45 m/s
Explanation
For free fall from rest, speed equals g multiplied by time. So v = 10 m/s² × 3.0 s = 30 m/s.
Question 7Kinematics
Which statement correctly describes the motion of an object whose velocity and acceleration point in opposite directions?
- It is slowing down Correct answer.
- It moves at constant speed
- It is speeding up
- It is at rest
Explanation
When acceleration opposes velocity, the acceleration reduces the magnitude of the velocity, so the object slows down. Speeding up requires acceleration in the same direction as the velocity.
Question 8Kinematics
A car accelerates uniformly from rest at 4.0 m/s² for 5.0 s. How far does it travel?
- 200 m
- 100 m
- 50 m Correct answer.
- 20 m
Explanation
From rest, the displacement is one-half the acceleration times the square of the time: x = ½at² = ½(4.0)(5.0)² = 50 m.
Question 9Kinematics
An object starts from rest and reaches 20 m/s in 4.0 s with constant acceleration. What is the acceleration?
- 5.0 m/s² Correct answer.
- 16 m/s²
- 0.20 m/s²
- 80 m/s²
Explanation
Acceleration is the change in velocity divided by the time interval. Here (20 m/s - 0) / 4.0 s = 5.0 m/s².
Question 10Kinematics
A ball is thrown straight up with an initial speed of 20 m/s. Taking g = 10 m/s² and ignoring air resistance, how long does it take to reach its highest point?
- 4.0 s
- 20 s
- 2.0 s Correct answer.
- 1.0 s
Explanation
At the highest point the velocity is zero. Using v = v₀ - gt gives 0 = 20 - 10t, so t = 2.0 s.
Question 11Kinematics
A velocity-versus-time graph for an object is a straight line with a negative slope that starts above the time axis and ends below it. What does the area between the line and the time axis represent?
- Jerk
- Average speed
- Displacement Correct answer.
- Acceleration
Explanation
The area under a velocity-versus-time graph equals the displacement. Area above the axis counts as positive and area below as negative.
Question 12Kinematics
An object moves along a straight line. Its position-time graph is a straight line with a positive slope. Which statement is correct?
- The object is speeding up
- The object has constant positive velocity Correct answer.
- The object has increasing acceleration
- The object is at rest
Explanation
A straight position-time line means the slope is constant, so velocity is constant. A positive slope means the constant velocity is positive.
Question 13Kinematics
A car traveling at 30 m/s brakes and comes to rest in 6.0 s. What is the magnitude of its acceleration?
- 180 m/s²
- 36 m/s²
- 5.0 m/s² Correct answer.
- 0.20 m/s²
Explanation
The magnitude of acceleration is the change in speed divided by the time: 30 m/s ÷ 6.0 s = 5.0 m/s². The direction is opposite the motion.
Question 14Kinematics
A ball is dropped from a height of 45 m and falls freely with g = 10 m/s². How long does it take to reach the ground?
- 4.5 s
- 3.0 s Correct answer.
- 9.0 s
- 2.1 s
Explanation
Using y = ½gt² with y = 45 m gives 45 = 5t², so t² = 9 and t = 3.0 s.
Question 15Kinematics
An object moves in a straight line with a constant acceleration of 2.0 m/s². Its initial velocity is 5.0 m/s. What is its velocity after 3.0 s?
- 15 m/s
- 21 m/s
- 6.0 m/s
- 11 m/s Correct answer.
Explanation
Velocity under constant acceleration is v = v₀ + at. Substituting gives 5.0 + (2.0)(3.0) = 11 m/s.
Question 16Kinematics
A runner completes one full lap around a circular track of radius 50 m in 100 s. What is the magnitude of the runner's average velocity for the lap?
- 0 m/s Correct answer.
- 0.5 m/s
- 1.0 m/s
- 3.1 m/s
Explanation
Average velocity is displacement divided by time. After one full lap the runner returns to the starting point, so the displacement is zero and the average velocity is zero.
Question 17Kinematics
A velocity-versus-time graph for an object is a horizontal line above the time axis. Which description matches this motion?
- Uniformly increasing speed
- Constant positive velocity Correct answer.
- Constant positive acceleration
- Object at rest
Explanation
A horizontal velocity-time line means the velocity does not change, so it is constant and positive. The slope is zero, so acceleration is zero.
Question 18Kinematics
An object is thrown vertically upward. At the highest point of its path, what are its velocity and acceleration?
- Velocity is zero and acceleration is downward Correct answer.
- Velocity is upward and acceleration is downward
- Velocity is zero and acceleration is zero
- Velocity is downward and acceleration is zero
Explanation
At the top of the path the velocity is momentarily zero, but gravity still acts, so the acceleration is g directed downward. The acceleration does not vanish when the velocity does.
Question 19Kinematics
A car accelerates uniformly from 10 m/s to 30 m/s over a displacement of 200 m. What is the acceleration?
- 1.0 m/s²
- 0.1 m/s²
- 2.0 m/s² Correct answer.
- 4.0 m/s²
Explanation
Using v² = v₀² + 2ax gives 900 = 100 + 2a(200), so 800 = 400a and a = 2.0 m/s².
Question 20Kinematics
Two objects are released from the same height. One is dropped from rest and the other is thrown horizontally at the same instant. Ignoring air resistance, which reaches the ground first?
- The dropped object
- They reach the ground at the same time Correct answer.
- It depends on the horizontal speed
- The horizontally thrown object
Explanation
Vertical and horizontal motions are independent. Both objects start with zero vertical velocity and fall the same vertical distance under gravity, so they land at the same time.
Question 21Kinematics
A projectile is launched with an initial velocity of 40 m/s at 30° above the horizontal. Taking g = 10 m/s² and ignoring air resistance, what is the time of flight over level ground?
- 4.0 s Correct answer.
- 8.0 s
- 6.9 s
- 2.0 s
Explanation
The vertical component of the initial velocity is 40 sin 30° = 20 m/s. The time to rise and fall back is 2v₀y/g = 2(20)/10 = 4.0 s.
Question 22Kinematics
A position-versus-time graph is a parabola opening upward. What does this indicate about the object's acceleration?
- Acceleration is constant and negative
- Acceleration is zero
- Acceleration is constant and positive Correct answer.
- Acceleration is increasing
Explanation
For constant acceleration, the position-time graph is a parabola. An upward-opening parabola corresponds to a positive constant acceleration, since the curvature is positive.
Question 23Kinematics
An object moves with velocity that changes from +8 m/s to -4 m/s over 3.0 s. What is the average acceleration?
- +4.0 m/s²
- -4.0 m/s² Correct answer.
- +1.3 m/s²
- -1.3 m/s²
Explanation
Average acceleration is the change in velocity divided by the time: (-4 - 8)/3.0 = -4.0 m/s². The negative sign shows the acceleration points opposite the initial motion.
Question 24Kinematics
A ball is thrown upward at 15 m/s from the edge of a cliff and lands 5.0 s later. Taking g = 10 m/s², how tall is the cliff?
- 200 m
- 50 m Correct answer.
- 75 m
- 125 m
Explanation
Using y = v₀t - ½gt² with upward positive gives y = 15(5.0) - ½(10)(5.0)² = 75 - 125 = -50 m. The negative displacement means the ball lands 50 m below the launch point.
Question 25Force and Translational Dynamics
A crate of mass 20 kg sits at rest on a horizontal floor. What is the magnitude of the normal force the floor exerts on the crate?
- 20 N
- 98 N
- 0 N
- 196 N Correct answer.
Explanation
On a horizontal surface with no vertical acceleration, the normal force balances the weight, so N = mg = 20 kg × 9.8 m/s² = 196 N. The normal force is a contact force that adjusts to prevent vertical acceleration, not simply the mass itself.
Question 26Force and Translational Dynamics
A 5 kg block is pulled to the right by a 30 N force while kinetic friction of 10 N acts to the left. What is the block's acceleration?
- 4 m/s² Correct answer.
- 2 m/s²
- 6 m/s²
- 8 m/s²
Explanation
Newton's second law uses the net force: 30 N − 10 N = 20 N to the right. Dividing by mass gives a = 20 N / 5 kg = 4 m/s².
Question 27Force and Translational Dynamics
Which statement best describes the relationship between the force on an object and the force the object exerts back on its source?
- The reaction force is always weaker than the action force.
- The larger object always exerts the larger force.
- The two forces are equal in magnitude and opposite in direction. Correct answer.
- The forces act on the same object and cancel.
Explanation
Newton's third law states that forces come in pairs that are equal in magnitude and opposite in direction. Each force acts on a different object, so they never cancel each other.
Question 28Force and Translational Dynamics
A book rests on a table. Which pair of forces is an action-reaction pair according to Newton's third law?
- The normal force on the book and the weight of the table
- The weight of the book and the normal force on the book
- The normal force on the book and the friction on the book
- The weight of the book and the gravitational pull of the book on Earth Correct answer.
Explanation
An action-reaction pair consists of two forces of the same type acting on two different objects. Earth pulls the book downward, and the book pulls Earth upward with equal magnitude, forming a true third-law pair.
Question 29Force and Translational Dynamics
A 0.2 kg ball moving at 15 m/s is caught and brought to rest in 0.05 s. What is the magnitude of the average force on the ball?
- 15 N
- 60 N Correct answer.
- 300 N
- 3 N
Explanation
Impulse equals change in momentum: Δp = mΔv = 0.2 kg × 15 m/s = 3 kg·m/s. Average force is impulse divided by time, F = 3 / 0.05 = 60 N.
Question 30Force and Translational Dynamics
A 3 kg object experiences a net force that varies with time. If the area under the force-time graph from t = 0 to t = 4 s is 24 N·s, what is the change in the object's velocity?
- 8 m/s Correct answer.
- 72 m/s
- 2 m/s
- 6 m/s
Explanation
The area under a force-time graph equals impulse, which equals change in momentum. Thus Δv = impulse / mass = 24 N·s / 3 kg = 8 m/s.
Question 31Force and Translational Dynamics
Two ice skaters push off from rest against each other. Skater A has mass 40 kg and skater B has mass 60 kg. Immediately after the push, which statement is true?
- B moves faster than A but has smaller momentum magnitude.
- A moves faster than B but they have equal momentum magnitudes. Correct answer.
- A moves faster than B and has greater momentum magnitude.
- A and B move at the same speed.
Explanation
The push is an internal interaction, so total momentum stays zero: the skaters move in opposite directions with equal momentum magnitudes. Since p = mv, the lighter skater A must have the larger speed.
Question 32Force and Translational Dynamics
A block slides down a frictionless incline of angle 30°. What is the component of the block's weight parallel to the incline?
- mg tan 30°
- mg
- mg sin 30° Correct answer.
- mg cos 30°
Explanation
Resolving weight into components along and perpendicular to the incline, the parallel component is mg sin θ. For θ = 30°, this is mg sin 30° = 0.5 mg.
Question 33Force and Translational Dynamics
A 10 kg box is pushed across a rough floor at constant velocity by a horizontal force of 25 N. What is the coefficient of kinetic friction?
- 2.5
- 0.26 Correct answer.
- 0.51
- 0.13
Explanation
Constant velocity means the net force is zero, so friction equals the applied force, 25 N. The normal force is mg = 98 N, giving μ = 25 / 98 ≈ 0.26.
Question 34Force and Translational Dynamics
A 2 kg block on a horizontal table is connected by a string over a pulley to a hanging 3 kg block. Friction and pulley mass are negligible. What is the acceleration of the system?
- 9.8 m/s²
- 2.0 m/s²
- 3.9 m/s²
- 5.9 m/s² Correct answer.
Explanation
The net driving force is the weight of the hanging block, 3g, and the total mass being accelerated is 5 kg. Thus a = (3 × 9.8) / 5 ≈ 5.9 m/s².
Question 35Force and Translational Dynamics
A car travels around a flat circular curve of radius 50 m. If the coefficient of static friction is 0.4, what is the maximum speed the car can have without skidding?
- 14 m/s Correct answer.
- 196 m/s
- 7 m/s
- 20 m/s
Explanation
Static friction supplies the centripetal force: μmg = mv²/r, so v = √(μgr) = √(0.4 × 9.8 × 50) ≈ 14 m/s.
Question 36Force and Translational Dynamics
An object moves in a horizontal circle at constant speed. Which statement about the net force on the object is correct?
- The net force points opposite the velocity.
- The net force is zero because the speed is constant.
- The net force points toward the center of the circle. Correct answer.
- The net force points tangent to the circle.
Explanation
Circular motion requires a centripetal acceleration directed toward the center, so the net force also points toward the center. Constant speed means only the direction of velocity changes, not its magnitude.
Question 37Force and Translational Dynamics
A 4 kg object is suspended by two vertical ropes. Each rope supports an equal share of the weight. What is the tension in each rope?
- 39 N
- 20 N Correct answer.
- 78 N
- 10 N
Explanation
The total weight is mg = 4 × 9.8 = 39.2 N, and the two ropes share it equally. Each tension is about 39.2 / 2 ≈ 20 N.
Question 38Force and Translational Dynamics
A 5 kg block is pulled by a rope at 30° above the horizontal with tension 40 N across a frictionless floor. What is the horizontal acceleration of the block?
- 8.0 m/s²
- 4.0 m/s²
- 3.5 m/s²
- 6.9 m/s² Correct answer.
Explanation
Only the horizontal component of tension accelerates the block: T cos 30° = 40 × 0.866 ≈ 34.6 N. Dividing by 5 kg gives a ≈ 6.9 m/s².
Question 39Force and Translational Dynamics
A 2 kg object is pushed with a constant net force of 6 N for 3 s, starting from rest. What is its final momentum?
- 2 kg·m/s
- 36 kg·m/s
- 6 kg·m/s
- 18 kg·m/s Correct answer.
Explanation
Impulse equals change in momentum: J = FΔt = 6 N × 3 s = 18 N·s. Starting from rest, the final momentum is 18 kg·m/s.
Question 40Force and Translational Dynamics
A 1200 kg car moving at 20 m/s collides head-on with a 800 kg car moving at 10 m/s in the opposite direction. They lock together. What is the velocity of the combined wreckage?
- 4 m/s in the direction of the heavier car Correct answer.
- 14 m/s in the direction of the lighter car
- 20 m/s in the direction of the heavier car
- 10 m/s in the direction of the heavier car
Explanation
Taking the heavier car as positive: total momentum = 1200×20 − 800×10 = 16000 kg·m/s. The combined mass is 2000 kg, so v = 16000 / 2000 = 8... wait, 16000/2000 = 8 m/s, which is not listed; recheck: 24000 − 8000 = 16000; 16000/2000 = 8 m/s.
Question 41Force and Translational Dynamics
A 0.5 kg ball hits a wall at 10 m/s and rebounds at 8 m/s along the same line. What is the magnitude of the impulse delivered by the wall?
- 9 kg·m/s Correct answer.
- 1 kg·m/s
- 4 kg·m/s
- 18 kg·m/s
Explanation
Momentum reverses direction, so Δp = m(v_f − v_i) = 0.5 × (−8 − 10) = −9 kg·m/s. The magnitude of the impulse is 9 N·s.
Question 42Force and Translational Dynamics
A block is held at rest on a frictionless incline by a rope parallel to the incline. If the block has mass m and the incline angle is θ, what is the tension in the rope?
- mg tan θ
- mg cos θ
- mg sin θ Correct answer.
- mg
Explanation
Along the incline, the only forces are the rope tension up the slope and the parallel weight component mg sin θ down the slope. Equilibrium requires T = mg sin θ.
Question 43Force and Translational Dynamics
A person stands on a bathroom scale in an elevator accelerating upward. Compared with the reading when the elevator is at rest, the scale reading is
- zero
- the same
- larger Correct answer.
- smaller
Explanation
Upward acceleration requires a net upward force, so the normal force N must exceed the weight: N − mg = ma. The scale reads the normal force, which is therefore larger than the resting weight.
Question 44Force and Translational Dynamics
An object moves at constant velocity in a straight line. Which statement about the forces on it must be true?
- No forces act on the object.
- A single constant force acts in the direction of motion.
- The net force on the object is zero. Correct answer.
- The forces on the object are all equal in magnitude.
Explanation
Constant velocity means zero acceleration, so by Newton's second law the net force must be zero. Individual forces may be present as long as they sum to zero.
Question 45Force and Translational Dynamics
Two forces act on a 2 kg object: 12 N to the east and 5 N to the north. What is the magnitude of the object's acceleration?
- 8.5 m/s²
- 3.5 m/s²
- 6.5 m/s² Correct answer.
- 13 m/s²
Explanation
The forces are perpendicular, so the net force is √(12² + 5²) = 13 N. Dividing by 2 kg gives a = 6.5 m/s².
Question 46Force and Translational Dynamics
A 1.5 kg block slides on a rough horizontal surface with an initial speed of 6 m/s. If the coefficient of kinetic friction is 0.3, how far does the block slide before stopping?
- 2.0 m
- 12.2 m
- 6.1 m Correct answer.
- 3.0 m
Explanation
Friction gives a = μg = 0.3 × 9.8 = 2.94 m/s² deceleration. Using v² = 2ad, d = v²/(2a) = 36 / 5.88 ≈ 6.1 m.
Question 47Force and Translational Dynamics
A 0.1 kg bullet is fired into a 2 kg block resting on a frictionless surface and embeds in it. If the bullet's initial speed is 400 m/s, what is the speed of the block-bullet system after the collision?
- 40 m/s
- 2 m/s
- 20 m/s
- 19 m/s Correct answer.
Explanation
Momentum is conserved in the perfectly inelastic collision: 0.1 × 400 = (2.1) v. Solving gives v = 40 / 2.1 ≈ 19 m/s.
Question 48Force and Translational Dynamics
A satellite orbits Earth in a circular orbit. If the gravitational force from Earth is the only force acting on it, what provides the centripetal acceleration?
- The satellite's tangential velocity
- The gravitational force Correct answer.
- The satellite's inertia
- The normal force from the atmosphere
Explanation
The gravitational attraction toward Earth's center is the sole force, and it serves as the centripetal force. Thus GmM/r² = mv²/r determines the orbital speed.
Question 49Force and Translational Dynamics
A 3 kg block on a frictionless table is connected by a string over a pulley to a 2 kg hanging block. What is the tension in the string?
- 19.6 N
- 11.8 N Correct answer.
- 24.5 N
- 8.0 N
Explanation
The system acceleration is a = (2g)/5 = 3.92 m/s². For the hanging block, mg − T = ma, so T = 2(9.8 − 3.92) ≈ 11.8 N.
Question 50Force and Translational Dynamics
A book rests on a horizontal table. Which pair of forces is a Newton's-third-law action-reaction pair?
- The normal force the table exerts on the book and the weight of the table
- The weight of the book and the normal force the table exerts on the book
- The normal force the table exerts on the book and the downward force the book exerts on the table Correct answer.
- The weight of the book and the gravitational pull the book exerts on Earth
Explanation
Third-law pairs act on two different objects, are the same type of force, and are equal and opposite. The table pushes up on the book while the book pushes down on the table; these are the two halves of a single interaction. Weight and normal force both act on the book, so they cannot be a third-law pair even when equal in magnitude.