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/ms and its initial velocity is 39 m/s. Find its displacement during the time interval from 𝑑=1 to 𝑑=9seconds.

Q2:

A particle moves along the π‘₯-axis in the direction of π‘₯ increasing. It starts at π‘₯=37cm 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 = 3 5 3 / c m s , s = 1 , 2 0 0 c m
  • B v = 2 0 0 / c m s , s = 9 6 5 c m
  • C v = 2 0 0 / c m s , s = 1 , 1 6 3 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 = 7 7 8 c m

Q3:

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.

Q4:

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.

Q5:

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.

Q6:

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

Q7:

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.

Q8:

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 π‘£οŠ¦ and its velocity 𝑣 at the end of this period.

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

Q9:

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

Q10:

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.

Q11:

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.

Q12:

If a particle which was moving in a straight line with an initial velocity π‘£οŠ¦ 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.

Q13:

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.

Q14:

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.

Q15:

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.

Q16:

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 traveled this distance.

Q17:

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?

Q18:

If a particle was moving with an initial velocity π‘£οŠ¦ and a constant acceleration π‘Ž, determine the average velocity of the particle during the 1st, 2nd, and 3rd seconds of its movement.

  • A 𝑣 + 1 . 5 π‘Ž 
  • B 𝑣 + 2 . 5 π‘Ž 
  • C 𝑣 + π‘Ž 
  • D 𝑣 + 3 π‘Ž 
  • E 𝑣 + 2 π‘Ž 

Q19:

A body started moving in a straight line from rest. It accelerated uniformly at 7 cm/s2 for 36 seconds, and then it continued moving at the velocity it had gained for a further 34 seconds. Find the magnitude of its average velocity 𝑣.

Q20:

A race car was moving at 91 m/s. It decelerated for 12 seconds until its velocity was 54 m/s. Determine the distance covered by the car while it was decelerating.

Q21:

A body was moving in a straight line with an initial velocity of 13 m/s and with an acceleration of 3 m/s2. Find the distance covered in the first 4 seconds.

Q22:

A car, moving in a straight line, decreased its velocity uniformly from 61 km/h to 24.4 km/h over 441 m. Given that it maintains a constant rate of deceleration, how much further will the car travel before it comes to rest?

Q23:

A cyclist, moving in a straight line, accelerated over a distance of 35.5 m until his velocity reached 10.8 m/s. Given that this took 5 seconds, find the cyclist’s initial velocity.

Q24:

A particle was moving in a straight line with a constant acceleration of 2 cm/s2. Given that its initial velocity was 60 cm/s, find the velocity of the body when it was 15 m from the starting point.

Q25:

A car decelerated from 144 km/h to 48 km/h. Given that while decelerating, it covered 1,200 m, find the time 𝑑 it took. If the car maintained this rate of deceleration, how much farther would it travel before it stops?

  • A 𝑑 = 2 2 . 5 s , 75 m
  • B 𝑑 = 1 1 . 2 5 s , 75 m
  • C 𝑑 = 4 5 s , 150 m
  • D 𝑑 = 1 2 . 5 s , 150 m

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