Worksheet: Kinematic Equations

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In this worksheet, we will practice applying the laws of the uniform acceleration motion of a particle in a straight line.

Q1:

A particle is moving in a straight line such that its acceleration π‘Ž = βˆ’ 3 / m s 2 and its initial velocity is 39 m/s. Find its displacement during the time interval from 𝑑 = 1 to 𝑑 = 9 s e c o n d s .

Q2:

The figure shown is a speed-time graph for a body moving in a straight line. Given that its initial speed was 5 m/s, determine the body’s acceleration during the part of the journey where the body was accelerating.

Q3:

The figure shown is a velocity-time graph for a body moving in a straight line with an initial velocity of 10 m/s. Determine the total distance covered by the body, given that it came to rest 100 seconds after it started moving.

Q4:

The figure shown is a velocity-time graph for a body moving in a straight line. Determine the deceleration of the body during the final section of its movement, given that it came to rest 100 seconds after it started moving.

Q5:

A particle moves along the π‘₯ -axis in the direction of π‘₯ increasing. It starts at π‘₯ = 3 7 c m with an initial velocity of 47 cm/s and moves with uniform acceleration of 51 cm/s2 in the same direction as its motion. Determine its velocity and its displacement from the origin after 6 seconds.

  • A v = 2 0 0 / c m s , s = 1 1 6 3 c m
  • B v = 3 5 3 / c m s , s = 1 2 0 0 c m
  • C v = 2 0 0 / c m s , s = 7 7 8 c m
  • D v = 3 5 3 / c m s , s = 1 2 3 7 c m
  • E v = 2 0 0 / c m s , s = 9 6 5 c m

Q6:

A particle was observed moving in a straight line. Its velocity was measured 7 seconds after it was first observed and was found to be 188 cm/s. It was measured again 22 seconds after the initial observation and was found to be 86 cm/s. Assuming that its acceleration was constant, find its initial velocity.

Q7:

A particle, accelerating uniformly at 50 cm/s2, was moving in a straight line. If its initial velocity was 45 km/h in the same direction as the acceleration, find the time required for it to cover 54 m.

Q8:

A particle started moving in a straight line at 7 m/s. Given that its acceleration was of magnitude 2 cm/s2 in the opposite direction to its movement, find the time taken for the particle to come to rest.

Q9:

A particle was moving in a straight line at 172.8 km/h. If it decelerated over 120 m to come to rest, find the deceleration π‘Ž of the particle and the time 𝑑 taken to cover this distance.

  • A π‘Ž = 9 . 6 / m s 2 , 𝑑 = 2 . 5 s
  • B π‘Ž = 1 9 . 2 / m s 2 , 𝑑 = 2 . 5 s
  • C π‘Ž = 1 9 . 2 / m s 2 , 𝑑 = 1 . 2 5 s
  • D π‘Ž = 9 . 6 / m s 2 , 𝑑 = 5 s

Q10:

Determine the time required for a particle to increase its velocity from 7 m/s to 18 m/s over a distance of 269 m, given that it is moving in a straight line with a uniform acceleration.

Q11:

The figure shown is a velocity-time graph for two cars moving in a straight line. The movement of car 𝐴 is represented by the green line, and the movement of car 𝐡 by the blue line. Determine how long it took for the two cars to meet again, given that they started from the same point.

Q12:

A particle, moving in a straight line, was accelerating at a rate of 22 cm/s2 in the same direction as its initial velocity. If the magnitude of its displacement 10 seconds after it started moving was 29 m, calculate the magnitude of its initial velocity 𝑣 0 and its velocity 𝑣 at the end of this period.

  • A 𝑣 = 2 . 3 5 / 0 m s , 𝑣 = 4 . 5 5 / m s
  • B 𝑣 = 4 / 0 m s , 𝑣 = 6 . 2 / m s
  • C 𝑣 = 7 . 3 / 0 m s , 𝑣 = 9 . 5 / m s
  • D 𝑣 = 1 . 8 / 0 m s , 𝑣 = 4 / m s

Q13:

A particle started accelerating from rest at 40 cm/s2. When its velocity reached 11 m/s, it started decelerating at a rate of 40 cm/s2 until it came to rest. Find the total time 𝑑 during which the particle was moving and the distance 𝑑 it covered.

  • A 𝑑 = 1 1 0 s , 𝑑 = 6 0 5 m
  • B 𝑑 = 5 5 s , 𝑑 = 6 0 5 m
  • C 𝑑 = 2 7 . 5 s , 𝑑 = 1 2 1 0 m
  • D 𝑑 = 5 5 s , 𝑑 = 3 0 2 . 5 m

Q14:

A body, moving in a straight line with a uniform acceleration of 2 m/s2, covered 136 m before it stopped accelerating. It continued to move at the velocity it had acquired for a further 27 seconds. Given that the total distance covered by the body was 1 162 m, find its initial velocity.

Q15:

A particle was decelerating in a straight line at a rate of 4 cm/s2. If it momentarily came to rest 10 seconds after it started moving, find the distance it covered in 18 seconds.

Q16:

A small ball was projected horizontally in the opposite direction of the wind at 42.9 cm/s to move in a straight line with a retardation of 7.5 cm/s2. Find the time taken for the ball to return back to the point of projection.

Q17:

A particle was moving with a constant acceleration π‘Ž such that it covered 750 cm in 12 seconds. When its acceleration was increased to 2 π‘Ž , it covered a further 500 cm in 4 seconds. After that, it started decelerating at a rate of 3 π‘Ž until it came to rest. Find the value of π‘Ž and the total distance covered by the particle π‘₯ .

  • A π‘Ž = 1 5 . 6 2 / c m s 2 , π‘₯ = 1 8 5 0 c m
  • B π‘Ž = 1 5 . 6 2 / c m s 2 , π‘₯ = 1 1 0 0 c m
  • C π‘Ž = 7 . 8 1 / c m s 2 , π‘₯ = 1 1 0 0 c m
  • D π‘Ž = 6 . 2 5 / c m s 2 , π‘₯ = 1 8 5 0 c m

Q18:

A particle, starting from rest, began moving in a straight line. It covered a distance of 125 m while accelerating uniformly at a rate of 10 m/s2. Then, maintaining the velocity that it had gained, it covered a distance of 479 m. Finally, it decelerated uniformly at a rate of 5 m/s2 until it came to rest. How long was the particle moving for?

Q19:

A body started moving in a straight line from rest. Accelerating uniformly, it covered 450 m until its speed became 50 m/s. Continuing at this velocity, it covered a further 500 m. Finally, it decelerated uniformly over 200 m until it came to rest. Find the acceleration π‘Ž of the body over its final 200 m and the time 𝑑 taken to cover the whole distance.

  • A π‘Ž = βˆ’ 2 5 / m s 2 , 𝑑 = 2 7 s
  • B π‘Ž = βˆ’ 1 2 . 5 / m s 2 , 𝑑 = 2 6 . 1 s
  • C π‘Ž = βˆ’ 0 . 2 5 / m s 2 , 𝑑 = 3 2 s
  • D π‘Ž = βˆ’ 6 . 2 5 / m s 2 , 𝑑 = 3 6 s

Q20:

If a particle which was moving in a straight line with an initial velocity 𝑣  started decelerating at a rate of 10 m/s2 such that it came to rest 5 seconds later, what would the body’s velocity be 6 seconds after it started decelerating? Let the direction of the initial velocity be the positive direction.

Q21:

Given that a particle started moving from rest with a constant acceleration of 3.5 m/s2 until its velocity became 378 km/h, find the distance it covered.

Q22:

A particle started moving in a straight line from rest with a uniform acceleration of 5.4 m/s2. Determine its velocity after 2 seconds from when it started moving.

Q23:

A car was moving in a straight line at 45 km/h. Given that the velocity decreased at a constant rate until the car came to rest 10 seconds after the driver hit the brakes, calculate the deceleration of the car.

Q24:

A particle started moving from rest in a straight line with a uniform acceleration of 15.3 cm/s2. If, whilst accelerating, it covered a distance of 7 cm, determine its velocity after it travelled this distance.

Q25:

A car that was moving in a straight line started slowing down. Its velocity decreased uniformly from 92 km/h to 52 km/h over 20 seconds. Given that it maintained a constant rate of deceleration, how much farther would the car travel before it came to rest?

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