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Akita Entrance Science study materials
Akita Entrance Science study resources

Akita Entrance Science practice questions

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Question 1Physics

A student walks 3.0 m east, then 4.0 m north. What is the magnitude of the resultant displacement?

  1. 1.0 m
  2. 7.0 m
  3. 12.0 m
  4. 5.0 m Correct answer.

Explanation

The two legs are perpendicular, so the resultant magnitude follows the Pythagorean relation: √(3.0² + 4.0²) = √25 = 5.0 m. Displacement is a vector, so the straight-line distance from start to finish is what matters, not the path length.

Question 2Physics

Which quantity is a scalar?

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

Explanation

A scalar has magnitude only, with no direction. Speed tells how fast something moves without stating a direction, whereas velocity, acceleration and displacement all require a direction to be fully specified.

Question 3Physics

An object moves at a constant velocity of 6.0 m/s for 5.0 s. How far does it travel?

  1. 30 m Correct answer.
  2. 1.2 m
  3. 25 m
  4. 11 m

Explanation

With constant velocity, distance equals speed multiplied by time: 6.0 m/s × 5.0 s = 30 m. Because the velocity does not change, no acceleration term is needed.

Question 4Physics

A car speeds up from rest to 20 m/s in 4.0 s. What is its average acceleration?

  1. 80 m/s²
  2. 0.20 m/s²
  3. 24 m/s²
  4. 5.0 m/s² Correct answer.

Explanation

Average acceleration is the change in velocity divided by the time taken: (20 − 0) / 4.0 = 5.0 m/s². The units follow from dividing m/s by s.

Question 5Physics

A ball is dropped from rest and falls freely near Earth's surface. Taking g = 9.8 m/s², what is its speed after 3.0 s, ignoring air resistance?

  1. 88 m/s
  2. 9.8 m/s
  3. 29 m/s Correct answer.
  4. 3.3 m/s

Explanation

For free fall from rest, speed equals g times time: 9.8 × 3.0 ≈ 29 m/s. Gravity adds about 9.8 m/s of speed every second, so after three seconds the speed is roughly three times that value.

Question 6Physics

Which statement best describes Newton's first law of motion?

  1. Force equals mass times acceleration.
  2. Every action has an equal and opposite reaction.
  3. The total momentum of an isolated system is conserved.
  4. An object remains at rest or in uniform motion unless a net force acts on it. Correct answer.

Explanation

Newton's first law states that an object keeps its state of rest or constant velocity unless a resultant force acts on it. This is often called the law of inertia, since it describes resistance to changes in motion.

Question 7Physics

A 4.0 kg block is pushed with a net force of 12 N on a frictionless surface. What is its acceleration?

  1. 48 m/s²
  2. 0.33 m/s²
  3. 16 m/s²
  4. 3.0 m/s² Correct answer.

Explanation

Newton's second law gives a = F/m, so 12 N ÷ 4.0 kg = 3.0 m/s². The net force is already given, so no friction term is subtracted.

Question 8Physics

Which of the following is an example of a contact force?

  1. The normal force from a table on a book Correct answer.
  2. The gravitational pull of the Moon on the sea
  3. The electrostatic repulsion between two protons
  4. The magnetic force on a moving charge

Explanation

A contact force acts only where two surfaces touch, such as the normal force a table exerts on a book. Gravity, electrostatic and magnetic forces act at a distance without physical contact.

Question 9Physics

A 2.0 kg ball moving at 3.0 m/s strikes a wall and rebounds at 2.0 m/s in the opposite direction. Taking the original direction as positive, what is the change in momentum?

  1. +2.0 kg·m/s
  2. −10 kg·m/s Correct answer.
  3. −2.0 kg·m/s
  4. +10 kg·m/s

Explanation

Initial momentum is 2.0 × 3.0 = +6.0 kg·m/s and final momentum is 2.0 × (−2.0) = −4.0 kg·m/s. The change is final minus initial: −4.0 − 6.0 = −10 kg·m/s, directed opposite to the original motion.

Question 10Physics

In a perfectly elastic collision between two identical trolleys, one moving at 2.0 m/s hits a stationary one head-on. Assuming no external forces, what happens after the collision?

  1. Both trolleys stop.
  2. The moving trolley stops and the other moves at 2.0 m/s. Correct answer.
  3. Both trolleys move together at 1.0 m/s.
  4. The moving trolley rebounds at 2.0 m/s and the other stays still.

Explanation

For a head-on elastic collision between equal masses, momentum and kinetic energy conservation together require the velocities to be exchanged. The incoming trolley stops and the struck trolley moves off at 2.0 m/s.

Question 11Physics

A 5.0 kg box is pushed along a rough floor at constant speed by a horizontal force of 20 N. What is the coefficient of kinetic friction?

  1. 0.20
  2. 0.41 Correct answer.
  3. 4.0
  4. 0.25

Explanation

At constant speed the pushing force balances friction, so friction is 20 N. The normal force equals the weight, 5.0 × 9.8 = 49 N, and μ = 20/49 ≈ 0.41.

Question 12Physics

A force of 50 N is applied at 60° above the horizontal to drag a crate. What is the horizontal component of the force?

  1. 43 N
  2. 50 N
  3. 87 N
  4. 25 N Correct answer.

Explanation

The horizontal component is F cos θ = 50 × cos 60° = 50 × 0.5 = 25 N. The vertical component would be F sin θ.

Question 13Physics

Two forces of 6.0 N and 8.0 N act at right angles on a point. What is the magnitude of their resultant?

  1. 2.0 N
  2. 10 N Correct answer.
  3. 48 N
  4. 14 N

Explanation

Perpendicular forces combine by the Pythagorean relation: √(6.0² + 8.0²) = √100 = 10 N. The resultant lies between the two forces in direction.

Question 14Physics

A 0.50 kg ball is thrown vertically upward with an initial speed of 10 m/s. Taking g = 9.8 m/s² and ignoring air resistance, what is the maximum height reached?

  1. 2.0 m
  2. 5.1 m Correct answer.
  3. 10 m
  4. 0.51 m

Explanation

At the highest point the speed is zero, so using v² = u² − 2gh gives h = u²/(2g) = 100/19.6 ≈ 5.1 m. Mass does not affect the height because gravity accelerates all masses equally.

Question 15Physics

A projectile is launched at 20 m/s at 30° above the horizontal on level ground. Taking g = 9.8 m/s², what is its horizontal range?

  1. 35 m Correct answer.
  2. 20 m
  3. 17 m
  4. 10 m

Explanation

The range formula is R = u² sin 2θ / g. Here sin 60° ≈ 0.866, so R = 400 × 0.866 / 9.8 ≈ 35 m.

Question 16Physics

A 60 W lamp is left on for 2.0 hours. How much energy does it transfer?

  1. 7.2 × 10³ J
  2. 120 J
  3. 4.3 × 10⁵ J Correct answer.
  4. 30 J

Explanation

Energy equals power times time, with time in seconds: 2.0 h = 7200 s, so E = 60 × 7200 = 4.32 × 10⁵ J. Using hours directly would give the wrong unit.

Question 17Physics

A 2.0 kg object is lifted 3.0 m at constant speed. Taking g = 9.8 m/s², how much gravitational potential energy does it gain?

  1. 29 J
  2. 6.0 J
  3. 59 J Correct answer.
  4. 20 J

Explanation

Gain in potential energy is mgh = 2.0 × 9.8 × 3.0 ≈ 59 J. Lifting at constant speed means the work done equals this gain exactly.

Question 18Physics

A machine does 600 J of useful work while consuming 800 J of energy. What is its efficiency?

  1. 75% Correct answer.
  2. 25%
  3. 133%
  4. 0.75 J

Explanation

Efficiency is useful output divided by total input: 600/800 = 0.75, or 75%. Efficiency is a ratio and is normally expressed as a percentage.

Question 19Physics

Two resistors of 4.0 Ω and 6.0 Ω are connected in parallel. What is the equivalent resistance?

  1. 1.5 Ω
  2. 2.4 Ω Correct answer.
  3. 10 Ω
  4. 0.42 Ω

Explanation

For two resistors in parallel, 1/R = 1/4.0 + 1/6.0 = 0.4167, giving R ≈ 2.4 Ω. The equivalent resistance is always smaller than the smallest branch resistor.

Question 20Physics

A charge of 12 C passes through a point in a circuit in 4.0 s. What is the current?

  1. 0.33 A
  2. 48 A
  3. 3.0 A Correct answer.
  4. 16 A

Explanation

Current is charge divided by time: I = Q/t = 12/4.0 = 3.0 A. The ampere is defined as one coulomb per second.

Question 21Physics

A 12 V battery is connected across a 3.0 Ω resistor. What power is dissipated in the resistor?

  1. 36 W
  2. 0.25 W
  3. 48 W Correct answer.
  4. 4.0 W

Explanation

Power can be found from P = V²/R = 144/3.0 = 48 W. Equivalently, the current is 4.0 A and P = VI = 12 × 4.0 = 48 W.

Question 22Physics

A block slides down a frictionless incline of height 2.0 m. Taking g = 9.8 m/s², what is its speed at the bottom if it starts from rest?

  1. 19.6 m/s
  2. 6.3 m/s Correct answer.
  3. 4.4 m/s
  4. 39 m/s

Explanation

By conservation of energy, mgh = ½mv², so v = √(2gh) = √(2 × 9.8 × 2.0) ≈ 6.3 m/s. The mass cancels, so the speed is independent of the block's mass.

Question 23Physics

A wave has a frequency of 50 Hz and a wavelength of 4.0 m. What is its speed?

  1. 54 m/s
  2. 200 m/s Correct answer.
  3. 0.080 m/s
  4. 12.5 m/s

Explanation

Wave speed equals frequency times wavelength: v = fλ = 50 × 4.0 = 200 m/s. This relation applies to all periodic waves in a uniform medium.

Question 24Physics

A sound wave travels from air into water, where its speed is greater. What happens to its frequency and wavelength?

  1. Frequency increases and wavelength stays the same.
  2. Frequency decreases and wavelength increases.
  3. Frequency stays the same and wavelength decreases.
  4. Frequency stays the same and wavelength increases. Correct answer.

Explanation

Frequency is set by the source and does not change when the wave enters a new medium. Since v = fλ and the speed rises while f is fixed, the wavelength must increase.

Question 25Physics

A ray of light strikes a plane mirror at 30° to the mirror surface. What is the angle of reflection, measured from the normal?

  1. 90°
  2. 120°
  3. 60° Correct answer.
  4. 30°

Explanation

Angles in reflection are measured from the normal, not the surface. If the ray makes 30° with the mirror, it makes 90° − 30° = 60° with the normal, and the reflected ray leaves at 60° to the normal.

Question 26Physics

A student measures the thickness of a metal plate five times and obtains 2.14 mm, 2.15 mm, 2.14 mm, 2.13 mm and 2.14 mm. Which statement about these measurements is most defensible?

  1. They are accurate but not precise.
  2. They are both precise and free from systematic error.
  3. They are precise but may still be inaccurate. Correct answer.
  4. They must contain a zero error in the instrument.

Explanation

Precision describes how closely repeated readings agree with one another, and these readings cluster tightly around 2.14 mm. Accuracy describes agreement with the true value, which cannot be judged without a reliable reference. Tight clustering therefore shows good precision but says nothing definite about accuracy.

Question 27Physics

A car travels 150 m due east and then 200 m due north. What is the magnitude of its displacement from the starting point?

  1. 250 m Correct answer.
  2. 350 m
  3. 175 m
  4. 50 m

Explanation

Displacement is a vector, so the two perpendicular legs form a right-angled triangle with the resultant as hypotenuse. Applying Pythagoras gives the square root of (150² + 200²), which equals 250 m. The direction would be about 53° north of east.

Question 28Physics

An object moves along a straight line with constant acceleration. Its velocity increases from 4.0 m/s to 16 m/s in 3.0 s. What is the acceleration?

  1. 6.7 m/s²
  2. 5.3 m/s²
  3. 4.0 m/s² Correct answer.
  4. 12 m/s²

Explanation

Acceleration is the change in velocity divided by the time taken. The change is 16 − 4.0 = 12 m/s over 3.0 s, giving 4.0 m/s². The value is positive because the speed is increasing in the direction of motion.

Question 29Physics

A book rests on a horizontal table. Which pair of forces is a Newton's-third-law action–reaction pair?

  1. The friction on the book and the normal force on the book
  2. The weight of the book and the normal force from the table on the book
  3. The weight of the book and the weight of the table
  4. The normal force from the table on the book and the push of the book on the table Correct answer.

Explanation

Third-law pairs act on two different bodies, are equal in magnitude, opposite in direction and of the same type. The table pushes the book upward while the book pushes the table downward with an equal contact force. The weight and normal force on the book both act on the same body, so they are not a third-law pair.

Question 30Physics

A satellite orbits Earth at constant speed. Which statement about the forces on the satellite is correct?

  1. The gravitational force is balanced by an outward force of equal size.
  2. A net force acts toward Earth, providing the centripetal acceleration. Correct answer.
  3. A net force acts along the direction of motion, keeping it moving.
  4. No force acts on it because its speed is constant.

Explanation

Constant speed along a circular path still means changing velocity direction, so the satellite accelerates toward the centre of the orbit. The gravitational pull of Earth supplies this centripetal force. Circular motion therefore requires a net force directed toward the centre, not zero force.

Question 31Physics

A spring obeys Hooke's law and extends by 4.0 cm when a 2.0 N force is applied. What force is needed to extend it by 10 cm within the elastic limit?

  1. 5.0 N Correct answer.
  2. 0.80 N
  3. 4.0 N
  4. 8.0 N

Explanation

Hooke's law states that extension is directly proportional to the applied force within the elastic limit. The spring constant is 2.0 N ÷ 0.040 m = 50 N/m. Extending it by 0.10 m therefore requires 50 × 0.10 = 5.0 N.

Question 32Physics

An electric kettle transfers 90 kJ of energy in 60 s. What is its power rating?

  1. 1.5 kW Correct answer.
  2. 5.4 MW
  3. 54 W
  4. 150 W

Explanation

Power is energy transferred per unit time, so 90 000 J divided by 60 s gives 1500 W. Expressed in kilowatts this is 1.5 kW. The large energy value is offset by the one-minute time interval.

Question 33Physics

A longitudinal wave travels along a stretched spring. Which feature of the wave corresponds to one full wavelength?

  1. The distance from a compression to the next rarefaction
  2. The time taken for one complete oscillation of a particle
  3. The distance between two adjacent compressions Correct answer.
  4. The maximum displacement of a particle from its rest position

Explanation

In a longitudinal wave the particles oscillate parallel to the direction of travel, producing compressions and rarefactions. One wavelength is the distance between successive compressions or successive rarefactions. The distance from a compression to the next rarefaction is only half a wavelength.

Question 34Physics

A 0.20 kg mass hangs at rest from a light spring and stretches it by 5.0 cm. Taking g = 9.8 m/s², what is the spring constant of the spring?

  1. 39 N/m Correct answer.
  2. 9.8 N/m
  3. 4.0 N/m
  4. 0.098 N/m

Explanation

At equilibrium the spring force balances the weight, so kx = mg. The weight is 0.20 × 9.8 = 1.96 N and the extension is 0.050 m. Dividing gives k = 1.96 ÷ 0.050 ≈ 39 N/m.

Question 35Physics

A 1200 kg car accelerates uniformly from rest to 20 m/s in 8.0 s. What is the average resultant force on the car?

  1. 2400 N
  2. 3000 N Correct answer.
  3. 96 000 N
  4. 150 N

Explanation

The acceleration is the change in velocity divided by the time, 20 ÷ 8.0 = 2.5 m/s². Newton's second law then gives F = ma = 1200 × 2.5 = 3000 N. This is the resultant force, so any resistive forces would have to be overcome by a larger driving force.

Question 36Physics

A 0.15 kg ball hits a wall horizontally at 12 m/s and rebounds horizontally at 8.0 m/s. The contact time is 0.050 s. What is the magnitude of the average force exerted by the wall on the ball?

  1. 36 N
  2. 24 N
  3. 12 N
  4. 60 N Correct answer.

Explanation

Taking the initial direction as positive, the change in velocity is −8.0 − 12 = −20 m/s, so the change in momentum is 0.15 × (−20) = −3.0 kg m/s. Dividing the magnitude by the contact time gives 3.0 ÷ 0.050 = 60 N. The large force arises because the momentum reverses in a very short time.

Question 37Physics

A uniform metre rule is pivoted at its centre. A 2.0 N weight hangs 30 cm to the left of the pivot. Where must a 3.0 N weight be placed to balance the rule?

  1. 30 cm to the right of the pivot
  2. 15 cm to the right of the pivot
  3. 20 cm to the right of the pivot Correct answer.
  4. 45 cm to the right of the pivot

Explanation

For rotational balance the anticlockwise moment must equal the clockwise moment. The left moment is 2.0 × 0.30 = 0.60 N m. Dividing by 3.0 N gives a distance of 0.20 m, so the weight must hang 20 cm to the right of the pivot.

Question 38Physics

A pump raises 500 kg of water through a height of 12 m every minute. Taking g = 9.8 m/s², what is the minimum output power of the pump?

  1. 4.9 kW
  2. 980 W Correct answer.
  3. 59 kW
  4. 410 W

Explanation

The useful work done is mgh = 500 × 9.8 × 12 = 58 800 J. This is delivered in 60 s, so the power is 58 800 ÷ 60 = 980 W. This is a minimum because real pumps also do work against friction in the pipes.

Question 39Physics

A 2.0 kg block slides from rest down a rough incline and reaches the bottom at 4.0 m/s after descending a vertical height of 1.5 m. Taking g = 9.8 m/s², how much energy is dissipated by friction?

  1. 13 J Correct answer.
  2. 45 J
  3. 16 J
  4. 29 J

Explanation

The loss in gravitational potential energy is mgh = 2.0 × 9.8 × 1.5 = 29.4 J. The kinetic energy gained is ½mv² = ½ × 2.0 × 16 = 16 J. The difference, about 13 J, must have been transferred to the surroundings by friction.

Question 40Physics

Two parallel plates 4.0 mm apart have a potential difference of 200 V between them. What is the electric field strength between the plates?

  1. 8.0 × 10⁻¹ V/m
  2. 5.0 × 10⁵ V/m
  3. 2.0 × 10³ V/m
  4. 5.0 × 10⁴ V/m Correct answer.

Explanation

For a uniform field between parallel plates, E = V/d. The separation must be in metres: 4.0 mm = 4.0 × 10⁻³ m. Dividing 200 V by 4.0 × 10⁻³ m gives 5.0 × 10⁴ V/m.

Question 41Physics

A 6.0 V battery of negligible internal resistance is connected to two resistors of 3.0 Ω and 6.0 Ω in series. What is the potential difference across the 6.0 Ω resistor?

  1. 4.0 V Correct answer.
  2. 6.0 V
  3. 2.0 V
  4. 3.0 V

Explanation

The series resistance is 3.0 + 6.0 = 9.0 Ω, so the current is 6.0 ÷ 9.0 = 0.667 A. The potential difference across the 6.0 Ω resistor is then 0.667 × 6.0 = 4.0 V. In a series circuit the larger resistance takes the larger share of the supply voltage.

Question 42Physics

A ray of light passes from glass of refractive index 1.5 into air. What is the critical angle for the glass–air boundary?

  1. 56°
  2. 48°
  3. 30°
  4. 42° Correct answer.

Explanation

At the critical angle the refracted ray grazes the boundary at 90°, so sin c = 1/n. For n = 1.5, sin c = 0.667, giving c ≈ 42°. Beyond this angle total internal reflection occurs.

Question 43Physics

A converging lens of focal length 10 cm forms an image of an object placed 15 cm from the lens. What are the image distance and nature of the image?

  1. 6.0 cm on the far side, virtual and upright
  2. 25 cm on the far side, real and inverted
  3. 30 cm on the same side, virtual and upright
  4. 30 cm on the far side, real and inverted Correct answer.

Explanation

Using 1/f = 1/u + 1/v with f = 10 cm and u = 15 cm gives 1/v = 1/10 − 1/15 = 1/30, so v = 30 cm. A positive image distance for a converging lens means a real image on the opposite side of the lens, and real images formed this way are inverted.

Question 44Physics

A transverse wave on a string has an amplitude of 3.0 cm and a wavelength of 0.80 m. It travels at 4.0 m/s. What is the frequency of the wave?

  1. 5.0 Hz Correct answer.
  2. 1.3 Hz
  3. 3.2 Hz
  4. 0.20 Hz

Explanation

The wave equation v = fλ relates speed, frequency and wavelength. Rearranging gives f = v/λ = 4.0 ÷ 0.80 = 5.0 Hz. The amplitude affects the energy carried by the wave but not its frequency.

Question 45Physics

A gas is compressed at constant temperature so that its volume halves. Which statement about the gas molecules is correct?

  1. Their mean kinetic energy is unchanged but they collide with the walls more frequently. Correct answer.
  2. Their mean speed halves because the volume halves.
  3. Their mean kinetic energy doubles because the pressure doubles.
  4. Their mean kinetic energy falls because the gas does work on the surroundings.

Explanation

For an ideal gas the mean kinetic energy of the molecules depends only on absolute temperature. At constant temperature the mean speed is therefore unchanged. Halving the volume increases the number of collisions with the container walls per second, which raises the pressure.

Question 46Physics

A radioactive source has a half-life of 8.0 days. What fraction of the original nuclei remains after 32 days?

  1. 1/32
  2. 1/16 Correct answer.
  3. 1/4
  4. 1/8

Explanation

The number of half-lives is 32 ÷ 8.0 = 4. After each half-life the remaining fraction is halved, so the fraction left is (1/2)⁴ = 1/16. Decay is random, so this is the expected fraction for a large sample.

Question 47Physics

A student connects a 12 V supply across a 4.0 Ω resistor and measures a current of 2.5 A. Which conclusion is best supported?

  1. The resistor obeys Ohm's law exactly.
  2. The supply has an internal resistance of about 0.80 Ω. Correct answer.
  3. The circuit contains no other resistance.
  4. The ammeter reading is impossible and must be a misreading.

Explanation

If the only resistance were 4.0 Ω, the current would be 12 ÷ 4.0 = 3.0 A. The measured 2.5 A implies a total resistance of 12 ÷ 2.5 = 4.8 Ω, so about 0.80 Ω is unaccounted for, consistent with internal resistance or connecting leads. The data are therefore physically reasonable once extra resistance is allowed.

Question 48Physics

A 0.50 kg trolley moving at 2.0 m/s collides with a stationary 1.5 kg trolley and they move off together. How much kinetic energy is lost in the collision?

  1. 0.25 J
  2. 1.0 J
  3. 0.75 J Correct answer.
  4. 1.5 J

Explanation

Momentum is conserved, so the common velocity is (0.50 × 2.0) ÷ 2.0 = 0.50 m/s. The initial kinetic energy is ½ × 0.50 × 4.0 = 1.0 J and the final kinetic energy is ½ × 2.0 × 0.25 = 0.25 J. The loss is therefore 0.75 J, which becomes heat and sound.

Question 49Physics

A projectile is fired at 25 m/s at 40° above the horizontal from level ground. Taking g = 9.8 m/s² and neglecting air resistance, what is the maximum height reached?

  1. 26 m
  2. 13 m Correct answer.
  3. 16 m
  4. 32 m

Explanation

The vertical component of velocity is 25 sin 40° ≈ 16.1 m/s. At the highest point the vertical velocity is zero, so h = u²/(2g) = 16.1² ÷ 19.6 ≈ 13 m. The horizontal component affects the range but not the maximum height.

Question 50Physics

Two identical resistors are connected first in series and then in parallel across the same battery of negligible internal resistance. How does the total power dissipated in the parallel arrangement compare with the series arrangement?

  1. It is twice as great.
  2. It is the same.
  3. It is half as great.
  4. It is four times greater. Correct answer.

Explanation

For two equal resistors R, the series resistance is 2R and the parallel resistance is R/2. Power from a fixed supply is V²/R_total, so the parallel arrangement draws four times the total resistance ratio's worth of power. Equivalently, the total resistance falls by a factor of four, so the power rises by a factor of four.