Lesson Worksheet: Applications on Motion with Uniform Acceleration Mathematics

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 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.

Q2:

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.

Q3:

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.

Q4:

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.

Q5:

A particle was moving in a straight line with a constant acceleration. If the particle covered 17 m in the 2nd second and 46 m in the 9th and 10th seconds, calculate its acceleration π‘Ž and its initial velocity π‘£οŠ¦.

  • Aπ‘Ž=4.44/ms, 𝑣=12.56/ms
  • Bπ‘Ž=0.8/ms, 𝑣=15.8/ms
  • Cπ‘Ž=5.33/ms, 𝑣=9/ms
  • Dπ‘Ž=0.67/ms, 𝑣=16.33/ms

Q6:

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.

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.

  • Aπ‘Ž=0.42/ms, 𝑣=33.6/ms
  • Bπ‘Ž=0.89/ms, 𝑣=71.2/ms
  • Cπ‘Ž=1.85/ms, 𝑣=148/ms
  • Dπ‘Ž=0.6/ms, 𝑣=48/ms

Q8:

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.

Q9:

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.

Q10:

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 π‘Ž in km/s2. If, under similar conditions, another bullet was fired at the wooden block that was 14 cm thick, determine the velocity 𝑣 at which the bullet exited the wooden block.

  • Aπ‘Ž=βˆ’20/kms, 𝑣=109.54/ms
  • Bπ‘Ž=βˆ’0.01/kms, 𝑣=80.02/ms
  • Cπ‘Ž=βˆ’10/kms, 𝑣=60/ms
  • Dπ‘Ž=βˆ’10/kms, 𝑣=95.92/ms

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