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AAPT NCPT (Level 1) study materials
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AAPT NCPT (Level 1) practice questions

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Question 1Mechanics

A car travels 150 m due east in 30 s. What is its average velocity?

  1. 4500 m/s east
  2. 5.0 m/s east Correct answer.
  3. 0.2 m/s east
  4. 4.5 m/s east

Explanation

Average velocity is displacement divided by elapsed time, and it carries the direction of the displacement. Dividing 150 m by 30 s gives 5.0 m/s directed east.

Question 2Mechanics

Which quantity is a vector?

  1. Temperature
  2. Speed
  3. Mass
  4. Displacement Correct answer.

Explanation

A vector has both magnitude and direction. Displacement specifies how far and in which direction an object moved, while speed, mass, and temperature are scalars with magnitude only.

Question 3Mechanics

An object moves at a constant velocity of 12 m/s for 5 s. How far does it travel?

  1. 17 m
  2. 7 m
  3. 2.4 m
  4. 60 m Correct answer.

Explanation

For constant velocity, distance equals speed multiplied by time. Multiplying 12 m/s by 5 s gives 60 m.

Question 4Mechanics

A ball is dropped from rest near Earth's surface, where g = 9.8 m/s^2. Ignoring air resistance, what is its speed after 3.0 s?

  1. 88.2 m/s
  2. 9.8 m/s
  3. 3.3 m/s
  4. 29.4 m/s Correct answer.

Explanation

Starting from rest, speed under constant acceleration equals acceleration times time. Multiplying 9.8 m/s^2 by 3.0 s gives 29.4 m/s.

Question 5Mechanics

According to Newton's first law, an object with zero net force acting on it will

  1. always come to rest
  2. maintain constant velocity Correct answer.
  3. move in a circle
  4. accelerate uniformly

Explanation

Newton's first law states that with zero net force, an object's velocity remains constant, which includes remaining at rest. It does not require the object to stop.

Question 6Mechanics

What is the SI unit of force?

  1. Pascal
  2. Joule
  3. Newton Correct answer.
  4. Watt

Explanation

Force is measured in newtons, where one newton accelerates one kilogram at one meter per second squared. The other units measure energy, power, and pressure respectively.

Question 7Mechanics

Two forces act on a point: 6 N to the right and 8 N at right angles to it (upward). What is the magnitude of the resultant force?

  1. 48 N
  2. 10 N Correct answer.
  3. 14 N
  4. 2 N

Explanation

Perpendicular forces combine by the Pythagorean theorem because they are orthogonal components. The resultant magnitude is the square root of 6^2 plus 8^2, which equals 10 N.

Question 8Mechanics

A 2 kg object is pushed with a net force of 10 N. What is its acceleration?

  1. 12 m/s^2
  2. 0.2 m/s^2
  3. 20 m/s^2
  4. 5 m/s^2 Correct answer.

Explanation

Newton's second law gives acceleration as net force divided by mass. Dividing 10 N by 2 kg yields 5 m/s^2.

Question 9Mechanics

A block slides down a frictionless incline that makes a 30-degree angle with the horizontal. Taking g = 9.8 m/s^2, what is the component of gravitational acceleration along the incline?

  1. 4.9 m/s^2 Correct answer.
  2. 9.8 m/s^2
  3. 8.5 m/s^2
  4. 5.7 m/s^2

Explanation

The acceleration along an incline is g times the sine of the incline angle. Since sine of 30 degrees is 0.5, the component is 4.9 m/s^2.

Question 10Mechanics

A 5 kg crate rests on a horizontal floor. The coefficient of static friction is 0.4. What is the minimum horizontal force needed to start it moving?

  1. 19.6 N Correct answer.
  2. 2.0 N
  3. 49 N
  4. 12.3 N

Explanation

The maximum static friction equals the coefficient times the normal force, and on a horizontal floor the normal force equals the weight. Thus 0.4 times 5 times 9.8 gives 19.6 N, the threshold force to overcome.

Question 11Mechanics

A 1200 kg car rounds a flat curve of radius 50 m at 15 m/s. What is the minimum coefficient of static friction required to prevent skidding?

  1. 0.90
  2. 0.46 Correct answer.
  3. 0.30
  4. 0.15

Explanation

The required centripetal force is provided by friction, so the coefficient equals v^2 divided by the product of g and radius. Computing 225 divided by 490 gives about 0.46.

Question 12Mechanics

A 0.5 kg ball moving at 8 m/s strikes a wall and rebounds at 6 m/s in the opposite direction. What is the magnitude of its change in momentum?

  1. 14 kg m/s
  2. 1 kg m/s
  3. 7 kg m/s Correct answer.
  4. 4 kg m/s

Explanation

Momentum is mass times velocity, and the reversal of direction means the velocities have opposite signs. The change is 0.5 times (8 plus 6), giving 7 kg m/s.

Question 13Mechanics

A 3 kg cart moving at 4 m/s collides and sticks to a 1 kg cart at rest. What is their common velocity after the collision?

  1. 2 m/s
  2. 4 m/s
  3. 1 m/s
  4. 3 m/s Correct answer.

Explanation

In a perfectly inelastic collision, momentum is conserved: total initial momentum equals total final momentum. The initial momentum is 12 kg m/s, and dividing by the combined 4 kg mass gives 3 m/s.

Question 14Mechanics

A worker lifts a 20 kg box 1.5 m vertically at constant speed. Taking g = 9.8 m/s^2, how much work does the worker do on the box?

  1. 13 J
  2. 294 J Correct answer.
  3. 196 J
  4. 30 J

Explanation

The worker applies an upward force equal to the box's weight over the vertical displacement. Work equals force times displacement, so 20 times 9.8 times 1.5 gives 294 J.

Question 15Mechanics

A 0.2 kg ball is thrown upward with 10 J of kinetic energy. Ignoring air resistance, how high does it rise?

  1. 5.1 m Correct answer.
  2. 10 m
  3. 0.5 m
  4. 2.0 m

Explanation

All kinetic energy converts to gravitational potential energy at the top, so height equals energy divided by the product of mass and g. Dividing 10 J by 0.2 times 9.8 gives about 5.1 m.

Question 16Mechanics

A machine does 600 J of useful work while consuming 1500 J of energy input. What is its efficiency?

  1. 60 percent
  2. 250 percent
  3. 40 percent Correct answer.
  4. 25 percent

Explanation

Efficiency is the ratio of useful output work to total input energy, expressed as a percentage. Dividing 600 by 1500 gives 0.40, or 40 percent.

Question 17Mechanics

A lever has an effort arm of 2.0 m and a load arm of 0.5 m. What is its ideal mechanical advantage?

  1. 2.5
  2. 4.0 Correct answer.
  3. 1.5
  4. 0.25

Explanation

For a lever, ideal mechanical advantage equals effort arm length divided by load arm length. Dividing 2.0 m by 0.5 m gives 4.0.

Question 18Mechanics

A uniform meter stick is balanced at its center. A 2 N weight hangs 20 cm to the left of the pivot. Where must a 4 N weight be placed to balance it?

  1. 20 cm right of the pivot
  2. 5 cm right of the pivot
  3. 10 cm right of the pivot Correct answer.
  4. 40 cm right of the pivot

Explanation

For rotational equilibrium, the torques about the pivot must be equal in magnitude. The left torque is 2 N times 20 cm, so the 4 N weight must sit 40 divided by 4, or 10 cm, from the pivot.

Question 19Mechanics

An object has a weight of 98 N on Earth, where g = 9.8 m/s^2. What is its mass?

  1. 0.1 kg
  2. 10 kg Correct answer.
  3. 960 kg
  4. 98 kg

Explanation

Weight is mass times gravitational acceleration, so mass equals weight divided by g. Dividing 98 N by 9.8 m/s^2 gives 10 kg.

Question 20Mechanics

Two satellites orbit Earth at different radii. The satellite in the larger orbit has

  1. a smaller orbital speed Correct answer.
  2. the same orbital speed
  3. a shorter orbital period
  4. a greater orbital speed

Explanation

For circular orbits, gravitational force supplies the centripetal requirement, giving orbital speed proportional to the inverse square root of the orbital radius. A larger radius therefore means a smaller speed.

Question 21Mechanics

A projectile is launched horizontally from a height with no air resistance. Which statement about its motion is correct?

  1. Both horizontal and vertical velocities increase equally
  2. Vertical velocity stays constant while horizontal velocity increases
  3. Horizontal velocity stays constant while vertical velocity increases Correct answer.
  4. Both horizontal and vertical velocities stay constant

Explanation

With no air resistance, no horizontal force acts, so horizontal velocity is constant. Gravity acts vertically, so the vertical velocity grows at rate g.

Question 22Mechanics

A 2 kg block on a frictionless horizontal surface is attached to a spring of constant 200 N/m and displaced 0.1 m from equilibrium, then released. What is its maximum speed?

  1. 20 m/s
  2. 0.5 m/s
  3. 1.0 m/s Correct answer.
  4. 10 m/s

Explanation

The stored spring energy converts entirely to kinetic energy at equilibrium. Setting the spring potential energy equal to kinetic energy gives a speed of the amplitude times the square root of stiffness over mass, which is 0.1 times 10, or 1.0 m/s.

Question 23Mechanics

A 4 kg object moving at 3 m/s collides elastically head-on with a 2 kg object at rest. What is the velocity of the 4 kg object after the collision?

  1. 0 m/s
  2. 2 m/s opposite its original direction
  3. 3 m/s in its original direction
  4. 1 m/s in its original direction Correct answer.

Explanation

For a head-on elastic collision, the final velocity of the heavier mass is the mass difference over the total mass times its initial velocity. Computing (4 minus 2) over 6 times 3 gives 1 m/s in the original direction.

Question 24Mechanics

A 0.1 kg ball hits a wall at 10 m/s and rebounds at 10 m/s, with contact lasting 0.02 s. What is the magnitude of the average force on the ball?

  1. 100 N Correct answer.
  2. 200 N
  3. 5 N
  4. 50 N

Explanation

Impulse equals the change in momentum and also equals average force times contact time. The momentum change is 0.1 times 20, or 2 kg m/s, and dividing by 0.02 s gives 100 N.

Question 25Mechanics

A block slides down a rough incline at constant speed. Which statement best describes the forces on the block?

  1. The net force points down the incline and exceeds friction
  2. The normal force equals the weight of the block
  3. Kinetic friction exceeds the downhill gravity component
  4. The net force is zero and the component of gravity along the incline equals kinetic friction Correct answer.

Explanation

Constant velocity means zero acceleration, so the net force must be zero. Along the incline, the downhill component of gravity is exactly balanced by kinetic friction.

Question 26Mechanics

A ball is thrown straight up into the air and returns to the thrower's hand. Ignoring air resistance, at the highest point of its path which quantity is zero?

  1. Its acceleration
  2. Its velocity Correct answer.
  3. Its gravitational potential energy
  4. Its mass

Explanation

At the top of the path the ball momentarily stops before reversing direction, so its instantaneous velocity is zero. Its acceleration remains g downward throughout the flight, and its potential energy is at a maximum there.

Question 27Mechanics

A runner completes one full lap of a circular track of radius 40 m in 50 s. What is the magnitude of the runner's average velocity for the lap?

  1. 2.5 m/s
  2. 0 m/s Correct answer.
  3. 5.0 m/s
  4. 1.6 m/s

Explanation

Average velocity is displacement divided by time. After one complete lap the runner returns to the starting point, so the displacement is zero and the average velocity is zero, even though the average speed is nonzero.

Question 28Mechanics

Which of the following is a scalar quantity?

  1. Acceleration
  2. Velocity
  3. Speed Correct answer.
  4. Displacement

Explanation

Speed has magnitude only and no direction, so it is a scalar. Velocity, acceleration, and displacement all require a direction to be fully specified and are vectors.

Question 29Mechanics

An object moves along a straight line with constant acceleration. Its velocity-time graph is a straight line that crosses the time axis. What does the point where the graph crosses the time axis represent?

  1. The instant the object reverses direction Correct answer.
  2. The instant the object comes permanently to rest
  3. The instant the acceleration becomes zero
  4. The instant the displacement is maximum

Explanation

On a velocity-time graph the sign of the velocity indicates direction. Where the line crosses the time axis the velocity passes through zero and changes sign, so the object reverses direction. The acceleration (the slope) is unchanged at that instant.

Question 30Mechanics

A 10 kg box is pulled across a horizontal floor by a rope that makes a 30-degree angle above the horizontal, with a tension of 50 N. What is the horizontal component of the tension?

  1. 43 N Correct answer.
  2. 25 N
  3. 29 N
  4. 50 N

Explanation

The horizontal component of a force at angle theta to the horizontal is F cos(theta). Here 50 N times cos 30 degrees equals about 43 N.

Question 31Mechanics

A 4 kg block sits on a horizontal table. A string over a pulley at the table edge connects it to a hanging 2 kg mass. The table is frictionless. Taking g = 10 m/s^2, what is the acceleration of the system?

  1. 2.0 m/s^2
  2. 5.0 m/s^2
  3. 10 m/s^2
  4. 3.3 m/s^2 Correct answer.

Explanation

The only external force driving the system is the weight of the hanging mass, 20 N. This accelerates the total mass of 6 kg, giving a = 20/6, about 3.3 m/s^2.

Question 32Mechanics

A 5 kg object is moving at 6 m/s. A constant net force of 10 N opposite to its motion acts on it. How long does it take to bring the object to rest?

  1. 1.2 s
  2. 3 s Correct answer.
  3. 0.5 s
  4. 30 s

Explanation

The acceleration is F/m = 10/5 = 2 m/s^2 directed opposite the motion. The time to stop is v/a = 6/2 = 3 s, from the kinematic relation v = v0 + at.

Question 33Mechanics

A 60 kg person stands on a bathroom scale inside an elevator. Taking g = 10 m/s^2, what does the scale read when the elevator accelerates upward at 2 m/s^2?

  1. 600 N
  2. 480 N
  3. 120 N
  4. 720 N Correct answer.

Explanation

The scale reads the normal force. Newton's second law gives N - mg = ma, so N = m(g + a) = 60 times 12 = 720 N.

Question 34Mechanics

Two ice skaters push off from each other while initially at rest on frictionless ice. The skater of mass 40 kg moves away at 3 m/s. What is the speed of the 60 kg skater?

  1. 3 m/s
  2. 1.5 m/s
  3. 4.5 m/s
  4. 2 m/s Correct answer.

Explanation

The skaters exert equal and opposite forces on each other, so total momentum stays zero. Thus 40 times 3 equals 60 times v, giving v = 2 m/s.

Question 35Mechanics

A 3 kg object moving at 4 m/s collides with a 5 kg object at rest. After the collision the two objects move together. How much kinetic energy is lost in the collision?

  1. 9 J
  2. 15 J Correct answer.
  3. 24 J
  4. 0 J

Explanation

Initial momentum is 12 kg m/s, so the common velocity is 12/8 = 1.5 m/s. Initial kinetic energy is 24 J and final is 0.5 times 8 times 1.5 squared, or 9 J, leaving 15 J lost.

Question 36Mechanics

A spring of negligible mass obeys Hooke's law and stores 4 J of elastic potential energy when compressed by 0.2 m. What is the spring constant?

  1. 100 N/m
  2. 200 N/m Correct answer.
  3. 40 N/m
  4. 20 N/m

Explanation

Elastic potential energy is U = (1/2)kx^2. Solving 4 = 0.5 times k times 0.04 gives k = 200 N/m.

Question 37Mechanics

A ball rolls off a horizontal table at 3 m/s and lands on the floor 0.8 s later. Taking g = 10 m/s^2, how far horizontally from the table edge does it land?

  1. 2.4 m Correct answer.
  2. 3.2 m
  3. 4.0 m
  4. 1.2 m

Explanation

The horizontal motion has constant velocity, so the horizontal distance is vx times t = 3 times 0.8 = 2.4 m. The vertical fall does not affect the horizontal range.

Question 38Mechanics

A 2 kg object moves in a circle of radius 3 m at a constant speed of 6 m/s. What is the magnitude of the net force required to keep it in this motion?

  1. 12 N
  2. 24 N Correct answer.
  3. 72 N
  4. 4 N

Explanation

For uniform circular motion the net force is centripetal, F = mv^2/r = 2 times 36 divided by 3, which is 24 N directed toward the center.

Question 39Mechanics

A uniform beam of weight 200 N is supported at each end by two vertical posts, one at the left end and one 2 m from the left end. A 300 N load hangs 1 m from the left end. The beam is in equilibrium. What is the upward force exerted by the left support?

  1. Equal to the total weight of 500 N
  2. It cannot be determined without the beam's length Correct answer.
  3. Zero, because the load is closer to the right support
  4. Equal to the force at the right support in all cases

Explanation

The torque balance depends on the positions of the beam's center of gravity and the supports, and the beam's length is needed to locate its center of gravity. Without that length the torque equation cannot be solved for the support forces, even though their sum must equal 500 N.

Question 40Mechanics

Two blocks of masses 3 kg and 2 kg are connected by a light string over a frictionless pulley, with the 3 kg block hanging on one side and the 2 kg block on the other. Taking g = 10 m/s^2, what is the tension in the string?

  1. 30 N
  2. 24 N Correct answer.
  3. 12 N
  4. 20 N

Explanation

The system accelerates at (3-2)g/(3+2) = 2 m/s^2. Applying Newton's second law to the 2 kg block gives T - 20 = 2 times 2, so T = 24 N.

Question 41Thermodynamics and Kinetic Theory

A sealed rigid container holds an ideal gas. If the absolute temperature of the gas is doubled while the volume is held constant, what happens to the pressure?

  1. It stays the same.
  2. It is halved.
  3. It doubles. Correct answer.
  4. It quadruples.

Explanation

For a fixed amount of ideal gas at constant volume, pressure is directly proportional to absolute temperature (Gay-Lussac's law). Doubling the absolute temperature therefore doubles the pressure.

Question 42Thermodynamics and Kinetic Theory

Which quantity is a measure of the average translational kinetic energy of the molecules of an ideal gas?

  1. Number of moles
  2. Absolute temperature Correct answer.
  3. Volume
  4. Pressure

Explanation

The average translational kinetic energy of ideal-gas molecules is (3/2)kT, which depends only on absolute temperature. Temperature is thus the direct macroscopic measure of that mean kinetic energy.

Question 43Thermodynamics and Kinetic Theory

In an isothermal process for an ideal gas, which statement about the internal energy is correct?

  1. It changes only if work is done on the gas.
  2. It decreases as the gas expands.
  3. It increases in proportion to the volume.
  4. It remains constant. Correct answer.

Explanation

For an ideal gas the internal energy depends only on temperature. An isothermal process holds temperature constant, so the internal energy does not change regardless of the volume change.

Question 44Thermodynamics and Kinetic Theory

Heat is added to a gas in a cylinder, and the gas does work on a piston while its internal energy changes. Which relation correctly expresses the first law of thermodynamics for the gas?

  1. ΔU = Q + W
  2. W = Q + ΔU
  3. Q = ΔU + W Correct answer.
  4. Q = ΔU − W

Explanation

The first law states that heat added to a system equals the increase in internal energy plus the work done by the system. With Q the heat added and W the work done by the gas, Q = ΔU + W.

Question 45Thermodynamics and Kinetic Theory

Two containers hold the same ideal gas at the same temperature and pressure, but one has twice the volume of the other. How do the numbers of molecules compare?

  1. The larger container holds half as many molecules.
  2. The larger container holds twice as many molecules. Correct answer.
  3. Both containers hold the same number of molecules.
  4. The larger container holds four times as many molecules.

Explanation

At fixed temperature and pressure, the ideal gas law gives n = PV/(RT), so the number of moles is proportional to volume. Doubling the volume therefore doubles the number of molecules.

Question 46Thermodynamics and Kinetic Theory

A system absorbs 500 J of heat and does 200 J of work on its surroundings. What is the change in its internal energy?

  1. 300 J Correct answer.
  2. −300 J
  3. −700 J
  4. 700 J

Explanation

Using Q = ΔU + W with Q = 500 J and W = 200 J gives ΔU = Q − W = 300 J. The internal energy rises because more heat enters than work leaves.

Question 47Thermodynamics and Kinetic Theory

Which process describes a change in which no heat is exchanged between a system and its surroundings?

  1. Isobaric
  2. Isothermal
  3. Isochoric
  4. Adiabatic Correct answer.

Explanation

An adiabatic process is defined by zero heat transfer between the system and its surroundings, so Q = 0. The other named processes constrain temperature, pressure, or volume instead.

Question 48Thermodynamics and Kinetic Theory

An ideal gas undergoes an isochoric heating. What is the work done by the gas?

  1. Zero Correct answer.
  2. Equal to the change in internal energy
  3. Equal to the pressure change times the volume
  4. Equal to the heat absorbed

Explanation

Work done by a gas is the integral of pressure over volume change. At constant volume the volume change is zero, so no work is done.

Question 49Thermodynamics and Kinetic Theory

The root-mean-square speed of molecules of an ideal gas is proportional to which quantity?

  1. The square of the absolute temperature
  2. The reciprocal of the absolute temperature
  3. The absolute temperature
  4. The square root of the absolute temperature Correct answer.

Explanation

The mean kinetic energy is (1/2)m(v_rms)^2 = (3/2)kT, so v_rms = sqrt(3kT/m). The rms speed therefore scales as the square root of absolute temperature.

Question 50Thermodynamics and Kinetic Theory

Two moles of an ideal monatomic gas are heated at constant volume so that the temperature rises by 100 K. Taking R = 8.31 J/(mol·K), what is the change in internal energy?

  1. 831 J
  2. 1662 J
  3. 2493 J Correct answer.
  4. 3324 J

Explanation

For a monatomic ideal gas ΔU = (3/2)nRΔT. Substituting n = 2, R = 8.31, and ΔT = 100 gives (3/2)(2)(8.31)(100) ≈ 2493 J.