Worksheet: Kinematic Equations

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?

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.