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SACE Stage 2 Physics study materials
SACE Stage 2 Physics study resources

SACE Stage 2 Physics practice questions

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Question 1Motion and Relativity

A car travels along a straight road at a constant velocity of 20 m/s for 15 s. What distance does it cover during this interval?

  1. 300 m Correct answer.
  2. 1.33 m
  3. 150 m
  4. 35 m

Explanation

For constant velocity, displacement equals velocity multiplied by time, so 20 m/s × 15 s = 300 m. Constant velocity means no acceleration term is needed in the calculation.

Question 2Motion and Relativity

Which of the following is a vector quantity?

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

Explanation

A vector requires both magnitude and direction, and displacement specifies how far and in which direction an object has moved. Speed, distance and time are scalars because they have magnitude only.

Question 3Motion and Relativity

An object is dropped from rest and falls freely near Earth's surface, where g = 9.8 m/s². What is its speed after 3.0 s, neglecting air resistance?

  1. 44 m/s
  2. 9.8 m/s
  3. 3.3 m/s
  4. 29 m/s Correct answer.

Explanation

Using v = u + at with u = 0 gives v = 9.8 × 3.0 = 29 m/s. Free fall near Earth's surface produces a constant downward acceleration of about 9.8 m/s².

Question 4Motion and Relativity

A ball is thrown vertically upward. At the highest point of its path, what are its velocity and acceleration?

  1. Velocity is zero and acceleration is 9.8 m/s² downward Correct answer.
  2. Velocity is zero and acceleration is zero
  3. Velocity is 9.8 m/s upward and acceleration is 9.8 m/s² downward
  4. Velocity is maximum and acceleration is zero

Explanation

At the top of the flight the vertical velocity is momentarily zero because the ball stops rising before falling. Gravity still acts, so the acceleration remains 9.8 m/s² directed downward throughout the motion.

Question 5Motion and Relativity

A stone is projected horizontally from a cliff at 12 m/s. Ignoring air resistance, what is its horizontal velocity 2.0 s later?

  1. 0 m/s
  2. 19.6 m/s
  3. 12 m/s Correct answer.
  4. 24 m/s

Explanation

With no air resistance there is no horizontal acceleration, so the horizontal velocity stays constant at 12 m/s. Gravity changes only the vertical component of velocity.

Question 6Motion and Relativity

A cyclist accelerates uniformly from 4.0 m/s to 12 m/s in 8.0 s. What is the magnitude of the acceleration?

  1. 1.0 m/s² Correct answer.
  2. 0.5 m/s²
  3. 8.0 m/s²
  4. 2.0 m/s²

Explanation

Acceleration equals the change in velocity divided by the time taken: (12 − 4.0) ÷ 8.0 = 1.0 m/s². This is the rate at which velocity increases each second.

Question 7Motion and Relativity

The area under a velocity–time graph represents which quantity?

  1. Acceleration
  2. Force
  3. Displacement Correct answer.
  4. Jerk

Explanation

Because velocity is the rate of change of displacement, the area under a velocity–time graph equals displacement. The gradient of the same graph gives acceleration instead.

Question 8Motion and Relativity

A body moves in a straight line with uniform acceleration. Which statement about its velocity–time graph is correct?

  1. It is a straight line with non-zero gradient Correct answer.
  2. It is a vertical line
  3. It is a horizontal line
  4. It is a curve of increasing slope

Explanation

Uniform acceleration means velocity changes at a constant rate, so the velocity–time graph is a straight line whose gradient equals the acceleration. A non-zero gradient shows the velocity is changing steadily.

Question 9Motion and Relativity

Which of the following is an inertial frame of reference?

  1. A frame in free fall toward Earth
  2. A frame rotating at constant angular speed
  3. A frame moving at constant velocity relative to the stars Correct answer.
  4. A frame accelerating uniformly in a straight line

Explanation

An inertial frame moves at constant velocity, so no acceleration is present and Newton's laws hold in their simple form. Accelerating, rotating and freely falling frames are all non-inertial.

Question 10Motion and Relativity

A spacecraft travels at 0.60c relative to Earth. According to the theory of special relativity, how does a clock on the spacecraft appear to run when observed from Earth?

  1. It runs faster than an Earth clock
  2. It runs slower than an Earth clock Correct answer.
  3. It runs at the same rate as an Earth clock
  4. It stops completely

Explanation

Time dilation means a moving clock runs slower as measured in the observer's frame, by the factor 1/√(1 − v²/c²). At 0.60c this factor is about 1.25, so the spacecraft clock appears to tick more slowly.

Question 11Motion and Relativity

An event lasts 10 s as measured in the rest frame of the observer. What is the proper time for this event?

  1. The longest time any observer measures
  2. The time measured in the frame where the event occurs at the same place Correct answer.
  3. The time measured in any frame moving relative to the event
  4. The time measured by an observer at the speed of light

Explanation

Proper time is the interval measured by an observer at rest relative to the event, that is, in the frame where the event occurs at a single location. It is the shortest time any observer measures.

Question 12Motion and Relativity

A rod has a proper length of 2.0 m. It moves at 0.80c parallel to its length relative to an observer. What length does the observer measure?

  1. 1.6 m
  2. 1.2 m Correct answer.
  3. 2.0 m
  4. 0.8 m

Explanation

Length contraction gives L = L₀√(1 − v²/c²) = 2.0 × √(1 − 0.64) = 2.0 × 0.60 = 1.2 m. Contraction occurs only along the direction of motion.

Question 13Motion and Relativity

What is the momentum of a 1500 kg car travelling at 20 m/s?

  1. 750 kg·m/s
  2. 15 000 kg·m/s
  3. 30 000 kg·m/s Correct answer.
  4. 75 kg·m/s

Explanation

Momentum equals mass multiplied by velocity, so p = 1500 × 20 = 30 000 kg·m/s. Momentum is a vector pointing in the direction of the car's motion.

Question 14Motion and Relativity

A 0.20 kg ball hits a wall at 10 m/s and rebounds at 8.0 m/s along the same line. Taking the initial direction as positive, what is the change in momentum of the ball?

  1. −0.4 kg·m/s
  2. +3.6 kg·m/s
  3. +0.4 kg·m/s
  4. −3.6 kg·m/s Correct answer.

Explanation

Initial momentum is 0.20 × 10 = +2.0 kg·m/s and final momentum is 0.20 × (−8.0) = −1.6 kg·m/s. The change is −1.6 − 2.0 = −3.6 kg·m/s, directed away from the wall.

Question 15Motion and Relativity

Two isolated trolleys collide and stick together. Which quantity is conserved in this collision?

  1. Total acceleration
  2. Total momentum Correct answer.
  3. Total speed
  4. Total kinetic energy

Explanation

In any collision between isolated bodies, total momentum is conserved because no external force acts on the system. A perfectly inelastic collision dissipates kinetic energy, so kinetic energy is not conserved.

Question 16Motion and Relativity

A 1200 kg car travelling at 15 m/s collides head-on with a stationary 800 kg car, and they lock together. What is their common velocity just after the collision?

  1. 9.0 m/s Correct answer.
  2. 12 m/s
  3. 6.0 m/s
  4. 15 m/s

Explanation

By conservation of momentum, 1200 × 15 = (1200 + 800) × v, so v = 18 000 ÷ 2000 = 9.0 m/s in the original direction. The combined mass is used because the cars lock together.

Question 17Motion and Relativity

A force of 200 N acts on a 50 kg object. What is the magnitude of its acceleration?

  1. 10 000 m/s²
  2. 4.0 m/s² Correct answer.
  3. 0.25 m/s²
  4. 150 m/s²

Explanation

Newton's second law gives a = F/m = 200 ÷ 50 = 4.0 m/s². The acceleration is in the same direction as the net force.

Question 18Motion and Relativity

A 5.0 kg block rests on a rough horizontal surface with a coefficient of kinetic friction of 0.30. What is the magnitude of the friction force when the block slides?

  1. 1.5 N
  2. 49 N
  3. 15 N Correct answer.
  4. 0 N

Explanation

The normal force equals the weight, mg = 5.0 × 9.8 = 49 N. The kinetic friction force is μN = 0.30 × 49 ≈ 15 N, opposing the sliding motion.

Question 19Motion and Relativity

An object moves in a circle at constant speed. Which statement about its acceleration is correct?

  1. It points tangentially to the circle
  2. It points toward the centre of the circle Correct answer.
  3. It points away from the centre of the circle
  4. It is zero because the speed is constant

Explanation

Even at constant speed the direction of velocity changes continuously, producing a centripetal acceleration directed toward the centre. Its magnitude is v²/r.

Question 20Motion and Relativity

A satellite orbits Earth at a radius r from Earth's centre. If the orbital radius is increased to 4r, how does the gravitational force on the satellite change?

  1. It becomes four times as large
  2. It becomes one half as large
  3. It becomes one sixteenth as large Correct answer.
  4. It becomes one quarter as large

Explanation

Newton's law of gravitation states that the force is inversely proportional to the square of the distance. Increasing the radius by a factor of four reduces the force by a factor of sixteen.

Question 21Motion and Relativity

A 2.0 kg object moves at 3.0 m/s. What is its kinetic energy?

  1. 6.0 J
  2. 9.0 J Correct answer.
  3. 12 J
  4. 18 J

Explanation

Kinetic energy is ½mv² = ½ × 2.0 × 3.0² = 9.0 J. The speed is squared, so the result depends strongly on velocity.

Question 22Motion and Relativity

A 60 kg student runs up a flight of stairs of vertical height 4.0 m in 5.0 s. Taking g = 9.8 m/s², what average power is developed?

  1. 2350 W
  2. 470 W Correct answer.
  3. 120 W
  4. 2940 W

Explanation

Work done against gravity is mgh = 60 × 9.8 × 4.0 = 2352 J, and power is work divided by time: 2352 ÷ 5.0 ≈ 470 W. Power measures the rate of doing work.

Question 23Motion and Relativity

In special relativity, the total energy of a particle at rest is given by which expression?

  1. ½mv²
  2. mv
  3. mc² Correct answer.
  4. mgh

Explanation

Einstein's mass–energy relation states that the rest energy of an object is E = mc². This shows that mass itself is a form of energy.

Question 24Motion and Relativity

A particle travels at 0.80c relative to an observer. What is the Lorentz factor γ for this motion?

  1. 0.60
  2. 1.25
  3. 1.67 Correct answer.
  4. 2.50

Explanation

The Lorentz factor is γ = 1/√(1 − v²/c²) = 1/√(1 − 0.64) = 1/0.60 ≈ 1.67. This factor scales time dilation, length contraction and relativistic mass.

Question 25Motion and Relativity

Two events occur at the same location in one inertial frame but at different times. In a second inertial frame moving relative to the first, which statement is always true?

  1. The time interval between them is longer than in the first frame Correct answer.
  2. The events occur at the same location
  3. The events occur in reverse order
  4. The events are simultaneous

Explanation

For events at the same place in one frame, that frame measures the proper time, which is the shortest possible interval. Any moving frame measures a longer, dilated time interval between the events.

Question 26Motion and Relativity

A runner completes one lap of a 400 m circular track in 80 s and finishes at the starting point. Which statement about the motion is correct?

  1. Both the average velocity and the average speed are zero.
  2. Both the average velocity and the average speed are 5.0 m/s.
  3. The average velocity is 5.0 m/s while the average speed is zero.
  4. The average velocity is zero while the average speed is 5.0 m/s. Correct answer.

Explanation

Average speed equals the total distance travelled divided by the time, giving 400 m divided by 80 s, which is 5.0 m/s. Average velocity depends on displacement, and because the runner returns to the starting point the displacement is zero, so the average velocity is also zero. The two quantities differ whenever the path is not a straight line.

Question 27Motion and Relativity

A stone is dropped from rest from a cliff and falls freely under gravity, taking g = 9.8 m/s². Ignoring air resistance, how far does it fall in the first 3.0 s?

  1. 29 m
  2. 44 m Correct answer.
  3. 9.8 m
  4. 88 m

Explanation

For motion from rest with constant acceleration, displacement equals one half of the acceleration multiplied by the square of the time. Substituting gives 0.5 × 9.8 × 3.0², which is 44.1 m, so 44 m to two significant figures. The initial velocity is zero so no extra term is needed.

Question 28Motion and Relativity

An object is projected horizontally from a table and lands on the floor. Neglecting air resistance, which statement describes its motion while airborne?

  1. The horizontal velocity stays constant while the vertical velocity increases uniformly. Correct answer.
  2. The horizontal and vertical velocities both remain constant.
  3. Both the horizontal and vertical velocities increase uniformly with time.
  4. The horizontal velocity decreases while the vertical velocity stays constant.

Explanation

With air resistance neglected, the only force acting after launch is the weight, which is vertical. There is no horizontal force, so the horizontal component of velocity is unchanged. The vertical component accelerates at g, so it grows uniformly from zero.

Question 29Motion and Relativity

A 0.50 kg ball moving at 6.0 m/s strikes a wall at right angles and rebounds at 4.0 m/s. What is the magnitude of the impulse delivered to the ball by the wall?

  1. 1.0 N s
  2. 5.0 N s Correct answer.
  3. 3.0 N s
  4. 11 N s

Explanation

Impulse equals the change in momentum, and momentum is a vector, so the reversal of direction must be included. Taking the initial direction as positive, the change is 0.50 × (−4.0) − 0.50 × (6.0), which is −5.0 kg m/s. The magnitude of the impulse is therefore 5.0 N s.

Question 30Motion and Relativity

A crate of mass 20 kg is pulled along a rough horizontal floor at constant velocity by a horizontal force of 60 N. What is the magnitude of the kinetic friction force acting on the crate?

  1. 30 N
  2. 0 N
  3. 200 N
  4. 60 N Correct answer.

Explanation

Constant velocity means the acceleration is zero, so the net horizontal force must be zero. The applied force and the kinetic friction force are the only horizontal forces, so they must be equal in magnitude and opposite in direction. Hence the friction force is 60 N.

Question 31Motion and Relativity

A car of mass 1000 kg rounds a flat circular bend of radius 50 m at a constant speed of 10 m/s. What is the magnitude of the centripetal force required?

  1. 500 N
  2. 2000 N Correct answer.
  3. 200 N
  4. 10 000 N

Explanation

The centripetal force needed for circular motion equals mass times speed squared divided by radius. Substituting gives 1000 × 10² / 50, which is 2000 N. This force is provided by friction between the tyres and the road surface.

Question 32Motion and Relativity

A moving object has momentum p and mass m. Which expression gives its kinetic energy in terms of these quantities?

  1. p/(2m)
  2. pm/2
  3. p²/(2m) Correct answer.
  4. 2p²/m

Explanation

Kinetic energy can be written as one half of mass times speed squared, and momentum is mass times speed. Substituting speed equals momentum divided by mass gives kinetic energy equal to momentum squared divided by twice the mass. This form is useful when momentum is known but speed is not.

Question 33Motion and Relativity

Light travels at c in a vacuum. According to the postulates of special relativity, what speed is measured for the same light pulse by an observer moving at 0.50c directly towards the source?

  1. 0.50c
  2. 0.75c
  3. 1.5c
  4. c Correct answer.

Explanation

A central postulate of special relativity is that the speed of light in a vacuum has the same value c in every inertial frame. This holds regardless of the motion of the source or of the observer. Velocities therefore do not simply add as they do at everyday speeds.

Question 34Motion and Relativity

A train moves at 0.80c relative to a platform. An observer on the platform measures the length of the train. Compared with the train's proper length, the measured length is

  1. shorter, because length contraction occurs along the direction of motion. Correct answer.
  2. longer, because the platform observer sees the front and rear at different times.
  3. longer, because the train's clocks run slow.
  4. the same, because length is an invariant quantity.

Explanation

Length contraction applies to the dimension parallel to the relative motion. The proper length is measured in the train's rest frame, and any frame moving relative to the object measures a shorter length. The contraction factor is the reciprocal of the Lorentz factor, so the effect grows as the speed approaches c.

Question 35Motion and Relativity

A particle moves at 0.60c relative to a laboratory. What is the Lorentz factor γ for this motion?

  1. 1.67
  2. 0.80
  3. 0.60
  4. 1.25 Correct answer.

Explanation

The Lorentz factor is one divided by the square root of one minus the speed ratio squared. For a speed of 0.60c the ratio squared is 0.36, so the square root of 0.64 is 0.80. Taking the reciprocal gives γ equal to 1.25.

Question 36Motion and Relativity

A muon has a proper lifetime of 2.2 μs and travels at 0.99c relative to Earth. Taking γ = 7.1, what is the approximate distance travelled through the atmosphere as measured in Earth's frame?

  1. 33 km
  2. 2.2 km
  3. 4.6 km Correct answer.
  4. 0.65 km

Explanation

In Earth's frame the muon's lifetime is dilated to γ times the proper lifetime, giving about 15.6 μs. The distance is then speed multiplied by this dilated time, that is 0.99 × 3.0 × 10⁸ × 15.6 × 10⁻⁶, which is roughly 4.6 km. Using the dilated lifetime is essential because the journey is measured in Earth's frame.

Question 37Motion and Relativity

A spacecraft of rest mass 2.0 × 10³ kg travels at 0.80c. Taking γ = 1.67, what is its relativistic momentum?

  1. 4.8 × 10¹¹ kg m/s
  2. 1.0 × 10¹² kg m/s
  3. 8.0 × 10¹¹ kg m/s Correct answer.
  4. 6.0 × 10¹¹ kg m/s

Explanation

Relativistic momentum equals the Lorentz factor multiplied by rest mass and speed. Here γ is 1.67, the mass is 2.0 × 10³ kg and the speed is 0.80 × 3.0 × 10⁸ m/s, which is 2.4 × 10⁸ m/s. Multiplying these gives approximately 8.0 × 10¹¹ kg m/s.

Question 38Motion and Relativity

In a particle accelerator, two protons approach each other head-on, each moving at 0.70c relative to the laboratory. Using the relativistic velocity addition formula, what is the speed of one proton relative to the other?

  1. 0.82c
  2. 1.40c
  3. 0.70c
  4. 0.94c Correct answer.

Explanation

Relativistic velocity addition gives the relative speed as the sum of the two speeds divided by one plus the product of their speed ratios. The numerator is 1.40c and the denominator is 1 + 0.49, which is 1.49. Dividing gives approximately 0.94c, always below c.

Question 39Motion and Relativity

A ball is thrown vertically upwards with a speed of 15 m/s. Taking g = 9.8 m/s² and neglecting air resistance, what is the maximum height reached above the release point?

  1. 11 m Correct answer.
  2. 23 m
  3. 1.5 m
  4. 15 m

Explanation

At the highest point the vertical velocity is momentarily zero. Using the relation that final speed squared equals initial speed squared minus twice the acceleration times the displacement gives a height of 15² divided by twice 9.8. This is approximately 11.5 m, so 11 m to two significant figures.

Question 40Motion and Relativity

A 3.0 kg trolley moving at 4.0 m/s to the right collides with a stationary 1.0 kg trolley, and they move off together. What is their common velocity after the collision?

  1. 4.0 m/s to the right
  2. 1.0 m/s to the right
  3. 12 m/s to the right
  4. 3.0 m/s to the right Correct answer.

Explanation

In an isolated collision total momentum is conserved, so the initial momentum of 3.0 × 4.0 equals 12 kg m/s. After the collision the combined mass is 4.0 kg, so the common velocity is 12 divided by 4.0. This gives 3.0 m/s in the original direction of motion.

Question 41Motion and Relativity

A 1500 kg car accelerates uniformly from rest to 20 m/s in 10 s along a level road. What is the average net force acting on the car?

  1. 30 000 N
  2. 300 N
  3. 3000 N Correct answer.
  4. 1500 N

Explanation

The acceleration is the change in velocity divided by the time, which is 20 divided by 10, giving 2.0 m/s². Newton's second law then gives the net force as mass times acceleration, that is 1500 × 2.0. This equals 3000 N.

Question 42Motion and Relativity

A satellite is in a circular orbit around Earth. If the orbital radius is doubled while the satellite's mass is unchanged, how does the gravitational force on the satellite change?

  1. It stays the same.
  2. It doubles.
  3. It falls to one quarter of its original value. Correct answer.
  4. It falls to one half of its original value.

Explanation

Newton's law of universal gravitation states that the force is inversely proportional to the square of the separation between the centres. Doubling the radius therefore divides the force by four. The satellite's mass does not affect how the force scales with radius.

Question 43Motion and Relativity

A spring of spring constant 200 N/m is compressed by 0.10 m and launches a 0.50 kg block along a frictionless horizontal surface. What is the speed of the block as it leaves the spring?

  1. 4.0 m/s
  2. 20 m/s
  3. 2.0 m/s Correct answer.
  4. 0.50 m/s

Explanation

The elastic potential energy stored in the spring is one half of the spring constant times the square of the compression. This is 0.5 × 200 × 0.10², which equals 1.0 J. All of this becomes kinetic energy, so the speed satisfies 0.5 × 0.50 × v² = 1.0, giving v = 2.0 m/s.

Question 44Motion and Relativity

A 2.0 kg object is lifted vertically at constant speed through a height of 3.0 m. Taking g = 9.8 m/s², what is the gain in gravitational potential energy?

  1. 59 J Correct answer.
  2. 6.0 J
  3. 20 J
  4. 0 J

Explanation

The gain in gravitational potential energy equals mass times gravitational field strength times the vertical height gained. Substituting gives 2.0 × 9.8 × 3.0, which is 58.8 J, or 59 J to two significant figures. The constant speed only means the lifting force balances the weight.

Question 45Motion and Relativity

A spring extends by 0.20 m when a force of 10 N is applied. What is the spring constant?

  1. 200 N/m
  2. 2.0 N/m
  3. 50 N/m Correct answer.
  4. 0.020 N/m

Explanation

Hooke's law states that the force exerted by a spring is proportional to its extension, with the spring constant as the constant of proportionality. Rearranging gives the spring constant as force divided by extension. This is 10 divided by 0.20, which equals 50 N/m.

Question 46Motion and Relativity

A rocket of rest mass M is at rest in deep space and emits a burst of light of energy E in one direction. What is the magnitude of the momentum carried away by the light?

  1. E/c²
  2. Ec
  3. Ec²
  4. E/c Correct answer.

Explanation

For a photon, or for any pulse of electromagnetic radiation, the momentum magnitude equals the energy divided by the speed of light. This follows from the relativistic energy-momentum relation with zero rest mass. The rocket must recoil with equal and opposite momentum to conserve total momentum.

Question 47Motion and Relativity

A particle has rest energy 4.0 MeV and total energy 5.0 MeV in a laboratory frame. What is its kinetic energy in that frame?

  1. 0.20 MeV
  2. 1.0 MeV Correct answer.
  3. 4.0 MeV
  4. 9.0 MeV

Explanation

The total relativistic energy of a particle equals its rest energy plus its kinetic energy. Rearranging gives kinetic energy as total energy minus rest energy. Subtracting 4.0 MeV from 5.0 MeV gives 1.0 MeV.

Question 48Motion and Relativity

Two events are simultaneous in one inertial frame and occur at different places along the x-axis. According to a second inertial frame moving relative to the first along the x-axis, which statement is correct?

  1. The events are generally not simultaneous in the second frame. Correct answer.
  2. The events are simultaneous only if the second frame moves at c.
  3. The events are always simultaneous in the second frame.
  4. The events occur at the same place in the second frame.

Explanation

The relativity of simultaneity states that events simultaneous in one frame are generally not simultaneous in a frame moving relative to it. The disagreement grows with the separation of the events and the relative speed. Only events that coincide in space as well as time are simultaneous in every frame.

Question 49Motion and Relativity

A particle of rest mass m travels at speed v such that its total energy is twice its rest energy. What is its speed?

  1. 0.99c
  2. 0.75c
  3. 0.50c
  4. 0.87c Correct answer.

Explanation

The total energy equals the Lorentz factor times the rest energy, so a total energy of twice the rest energy means γ equals 2. Squaring the Lorentz factor gives one over one minus the speed ratio squared equal to 4, so the speed ratio squared is 0.75. The speed ratio is therefore the square root of 0.75, which is about 0.87.

Question 50Motion and Relativity

In the laboratory frame, a particle moving at 0.60c decays with a lifetime of 5.0 μs. What is the proper lifetime of the particle?

  1. 4.0 μs Correct answer.
  2. 5.0 μs
  3. 6.25 μs
  4. 3.0 μs

Explanation

The proper lifetime is measured in the particle's own rest frame and is the shortest possible measured lifetime. The laboratory lifetime equals the proper lifetime multiplied by the Lorentz factor, which is 1.25 for 0.60c. Dividing 5.0 μs by 1.25 gives 4.0 μs.