# Worksheet: Kinematic Equations

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

**Q2: **

A particle moves along the -axis in the direction of
increasing. It starts at with an initial velocity
of 47 cm/s and moves with uniform acceleration
of 51 cm/s^{2} in the same direction as its
motion. Determine its velocity and its displacement from the origin after 6 seconds.

- A ,
- B ,
- C ,
- D ,
- E ,

**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/s^{2}, 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/s^{2} 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 of the particle and the time taken to cover this distance.

- A ,
- B ,
- C ,
- D ,

**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/s^{2} 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 and its velocity at the end of this period.

- A ,
- B ,
- C ,
- D ,

**Q9: **

A particle started accelerating from rest at 40 cm/s^{2}.
When its velocity reached 11 m/s,
it started decelerating at a rate of 40 cm/s^{2} until it came to rest.
Find the total time during which the particle was moving and the distance it covered.

- A ,
- B ,
- C ,
- D ,

**Q10: **

A particle was decelerating in a straight line at a rate of 4 cm/s^{2}.
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/s^{2}. 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
started decelerating at a rate of 10 m/s^{2}
such that it came to rest 5 seconds later, what would the bodyβs 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/s^{2}
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/s^{2}.
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/s^{2}.
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 and a constant acceleration , determine the average velocity of the particle during the 1st, 2nd, and 3rd seconds of its movement.

- A
- B
- C
- D
- E

**Q19: **

A body started moving in a straight line from rest. It accelerated uniformly at
7 cm/s^{2}
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 .

**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/s^{2}. 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 cyclistβs initial velocity.

**Q24: **

A particle was moving in a straight line with a constant acceleration of 2 cm/s^{2}.
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 it took. If the car maintained this rate of deceleration, how much farther would it travel before it stops?

- A , 75 m
- B , 75 m
- C , 150 m
- D , 150 m