Worksheet: Applications on Motion with Uniform Acceleration

In this worksheet, we will practice solving problems involving motion of a particle with uniform acceleration through one or more sections of its path.

Q1:

A man, driving his car at 28 m/s, saw a child crossing the road in front of him. Given that the man’s response time was 0.6 seconds and that after he struck the brakes, the car decelerated uniformly at a rate of 10 m/s2 until it stopped, find the total stopping distance of the car.

Q2:

A cyclist, riding down a hill from rest, was accelerating at a rate of 0.5 m/s2. By the time he reached the bottom of the hill, he was traveling at 1.5 m/s. He continued traveling at this speed for another 9.5 seconds. Determine the total distance 𝑠 that the cyclist covered.

Q3:

A body was moving in a straight line accelerating uniformly. If it covered 55 meters in the first 4 seconds and 57 meters in the next 4 seconds, determine the total distance that it covered in the first 10 seconds of its motion.

Q4:

A man was driving his car in a straight line at 78 km/h when he pressed the brakes. If the car’s velocity decreased at a constant rate until it stopped completely over a period of 15 seconds, determine the stopping distance of the car.

Q5:

A bullet was fired horizontally at 104 m/s into a vertical wall 10 cm thick. Given that it passed all the way through, and its exit velocity was 96 m/s, what was the magnitude π‘Ž of its deceleration which resulted from passing through the wall? If the bullet was fired with the same velocity into a similar vertical wall with the same resistance, how far would it penetrate before it came to a stop?

  • A π‘Ž = 1 6 / k m s , 135.2 cm
  • B π‘Ž = 8 / k m s , 135.2 cm
  • C π‘Ž = 8 / k m s , 67.6 cm
  • D π‘Ž = 1 6 / k m s , 67.6 cm

Q6:

A bullet was fired horizontally at a wooden block. It entered the block at 80 m/s and penetrated 32 cm into the block before it stopped. Assuming that its acceleration π‘Ž was uniform, find 𝑣. If, under similar conditions, another bullet was fired at the wooden block that was 14 cm thick, determine the velocity at which the bullet exited the wooden block.

  • A π‘Ž = βˆ’ 1 0 / k m s  , 𝑣 = 6 0 / m s
  • B π‘Ž = βˆ’ 2 0 / k m s  , 𝑣 = 1 0 9 . 5 4 / m s
  • C π‘Ž = βˆ’ 1 0 / k m s  , 𝑣 = 9 5 . 9 2 / m s
  • D π‘Ž = βˆ’ 0 . 0 1 / k m s  , 𝑣 = 8 0 . 0 2 / m s

Q7:

A train, starting from rest, began moving in a straight line between two stations. For the first 80 seconds, it moved with a constant acceleration π‘Ž. Then it continued to move at the velocity it had acquired for a further 65 seconds. Finally, it decelerated with a rate of 2π‘Ž until it came to rest. Given that the distance between the two stations was 8.9 km, find the magnitude of π‘Ž and the velocity 𝑣 at which it moved during the middle leg of the journey.

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

Q8:

A train was moving in a straight line between two stations 1,400 meters apart. It started moving from the first station by accelerating for 4 seconds at a rate of 1 m/s2. It then maintained its velocity until it decelerated uniformly over the last 50 meters to come to a stop at the final station. Find the time taken to travel between the two stations.

Q9:

A lift started to go up after resting at the bottom of a mine. It covered a distance of 479 m with an acceleration of 2.25 m/s2, then it moved with a uniform velocity for a distance of 720 m and finally with a uniform deceleration for a distance of 549 m until it reached the surface of the ground. Find the time the lift took from the bottom of the mine to reach the surface of the ground approximated to the nearest two decimal places, if needed.

Q10:

A body was moving in a straight line at a constant speed of 24 cm/s. 3 seconds after passing a certain point, another body started moving in the same direction from that point with an initial velocity of 18 cm/s and a uniform acceleration of 6 cm/s2. Find the time taken, in seconds, for the second body to catch up to the first.

Q11:

A small ball was moving in a straight line with a uniform velocity of 36 cm/s. 3 seconds after it passed a certain point, another ball started moving in the same direction with an initial velocity of 15 cm/s and a uniform acceleration of 5 cm/s2. Find the distance 𝑑 at which the two balls impact from the same starting point, and determine the velocity 𝑣 of the second ball just before the impact.

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

Q12:

A speeding car, moving at 96 km/h, passed by a police car. 12 seconds later, the police car started pursuing it. Accelerating uniformly, the police car covered a distance of 134 m until its velocity was 114 km/h. Maintaining this speed, it continued until it caught up with the speeding car. Find the time it took for the police car to catch the other car starting from the point the police car began moving.

Q13:

Two cars, 𝐴 and 𝐡, were moving toward each other on the same horizontal straight road. Car 𝐴 started from rest and accelerated uniformly at 3 m/s2, while car 𝐡 moved at a constant speed of 72 km/h. When the cars met, the relative velocity of car 𝐴 with respect to car 𝐡 was 180 km/h. Find the time the cars traveled to meet.

Q14:

A body, starting from rest, accelerated over 218 m until its velocity reached 72 km/h. After that it stopped accelerating and continued moving at this velocity for a further 44 m. Finally, it decelerated at a constant rate of 1 m/s2 until it stopped. Find the average velocity of the body during the whole trip.

Q15:

A particle initially at rest starts to move in a straight line with constant acceleration. When it has covered 350 m, its speed is 8 m/s. It covers another 797 m at this speed before slowing down with uniform retardation, coming to rest after traveling a further 192 m. Find 𝑑, the total time taken, and determine 𝑣, the average velocity for the whole journey. Give your answers correct to two decimal places.

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

Q16:

A child was practicing riding a bicycle. As a result of his father pushing him, he accelerated at a rate of 1.5 m/s2 for 2 seconds. Following this, he continued riding the bicycle at the speed he had gained for another 4 seconds. Find the distance that the child covered.

Q17:

A car, moving in a straight line at 72 km/h, passed a police car at rest. 18 seconds later, the police car began pursuing it. Accelerating uniformly, it attained a velocity of 102 km/h over 102 m. Continuing at this velocity, it pursued the car until it caught up. How far did the first car travel before the police car caught up with it?

Q18:

A body, moving in a straight line, covered 60 cm in 6 seconds whilst accelerating uniformly. Maintaining its velocity, it covered a further 52 cm in 5 seconds. Finally, it started decelerating at a rate double to the rate of its former acceleration until it came to rest. Find the total distance covered by the body.

Q19:

A body, moving in a straight line at 2 m/s, started accelerating uniformly at 7 m/s2 over a distance of 18 m. Then, maintaining this velocity, it covered a further 44 m. Find the time 𝑑 (in seconds) it took for the body to cover this distance and the distance π‘₯ covered by the body during its 2nd second of movement.

  • A 𝑑 = 1 8 . 4 6 s , π‘₯ = 9 . 8 8 m
  • B 𝑑 = 3 . 0 4 s , π‘₯ = 7 . 2 5 m
  • C 𝑑 = 4 . 7 5 s , π‘₯ = 1 2 . 5 m
  • D 𝑑 = 5 . 0 4 s , π‘₯ = 5 . 0 4 m

Q20:

A body started moving from rest with a steady acceleration of 0.1 m/s2. When its velocity reached 138 cm/s, it decelerated until it came to rest again 23 seconds after it started moving. Calculate the deceleration π‘Ž and the total distance 𝑑 covered by the body.

  • A π‘Ž = 0 . 1 9 / m s  , 𝑑 = 5 7 . 3 2 m
  • B π‘Ž = 0 . 1 9 / m s  , 𝑑 = 9 . 5 m
  • C π‘Ž = 0 . 1 5 / m s  , 𝑑 = 1 5 . 8 7 m
  • D π‘Ž = 0 . 3 5 / m s  , 𝑑 = 4 0 . 4 6 m

Q21:

A cyclist, riding down a hill from rest, was accelerating at a rate of 1.5 m/s2. By the time he reached the bottom of the hill, he was traveling at 9 m/s. He continued traveling at this speed for another 14 seconds. Determine the total distance 𝑠 that the cyclist covered.

Q22:

A body was projected vertically upwards at 12.74 m/s from the top of a tower. Find the time taken for the body to return to the point of projection. Consider the acceleration due to gravity to be 𝑔=9.8/ms.

Q23:

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.

Q24:

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?

Q25:

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

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