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In this lesson, we will learn how to solve problems on the applications of the laws of uniform acceleration motion in a straight line.

Q1:

A man, driving his car at 28 m/s, saw a child crossing the road in front of him. Given that the manβs response time was 0.6 seconds and that after he struck the brakes, the car decelerated uniformly at a rate of 10 m/s^{2} 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/s^{2}. By the time he reached the bottom of the hill, he was travelling at 1.5 m/s. He continued travelling at this speed for another 9.5 seconds. Determine the total distance π that the cyclist covered.

Q3:

A cyclist, riding down a hill from rest, was accelerating at a rate of 1.5 m/s^{2}. By the time he reached the bottom of the hill, he was travelling at 9 m/s. He continued travelling at this speed for another 14 seconds. Determine the total distance π that the cyclist covered.

Q4:

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/s^{2}. Find the distance π at which the two balls impact from the same starting point, and determine the velocity π£ of the second ball just before the impact.

Q5:

A small ball was moving in a straight line with a uniform velocity of 12 cm/s. 4 seconds after it passed a certain point, another ball started moving in the same direction with an initial velocity of 14 cm/s and a uniform acceleration of 5 cm/s^{2}. Find the distance π at which the two balls impact from the same starting point, and determine the velocity π£ of the second ball just before the impact.

Q6:

A child was practising riding a bicycle. As a result of his father pushing him, he accelerated at a rate of 1.5 m/s^{2} 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.

Q7:

If a particle was moving with an initial velocity π£ 0 and a constant acceleration π , determine the average velocity of the particle during the 1st, 2nd, and 3rd seconds of its movement.

Q8:

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?

Q9:

A child kicked a ball up a hill and waited until it rolled back down to him. Given that he kicked the ball at a speed of 112 cm/s and the effect of gravity resulted in a 5 m/s^{2} acceleration down the slope, find the time π‘ at which the ball momentarily came to rest and the displacement π₯ of the ball after 9 seconds.

Q10:

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.

Q11:

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 . Then it continued to move at the velocity it had acquired for a further 65 seconds. Finally, it decelerated with a rate of 2 π until it came to rest. Given that the distance between the two stations was 8.9 km, find the magnitude of π and the velocity π£ at which it moved during the middle leg of the journey.

Q12:

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

Q13:

Two cars, π΄ and π΅ , were moving towards each other on the same horizontal straight road. Car π΄ started from rest and accelerated uniformly at 3 m/s^{2}, while car π΅ moved at a constant speed of 72 km/h. When the cars met, the relative velocity of car π΄ with respect to car π΅ was 180 km/h. Find the time the cars travelled to meet.

Q14:

Two cars, π΄ and π΅ , were moving towards each other on the same horizontal straight road. Car π΄ started from rest and accelerated uniformly at 3 m/s^{2}, while car π΅ moved at a constant speed of 143 km/h. When the cars met, the relative velocity of car π΄ with respect to car π΅ was 305 km/h. Find the time the cars travelled to meet.

Q15:

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/s^{2}, 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.

Q16:

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 travelling a further 192 m. Find π‘ , the total time taken and determine π£ , the average velocity for the whole journey. Give your answers correct to two decimal places.

Q17:

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 was uniform, find π£ . 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.

Q18:

A bullet was fired horizontally at a wooden block. It entered the block at 102 m/s and penetrated 36 cm into the block before it stopped. Assuming that its acceleration π was uniform, find π£ . If, under similar conditions, another bullet was fired at the wooden block that was 20 cm thick, determine the velocity at which the bullet exited the wooden block.

Q19:

A train was moving in a straight line between two stations 1β400 metres apart. It started moving from the first station by accelerating for 4 seconds at a rate of 1 m/s^{2}. It then maintained its velocity until it decelerated uniformly over the last 50 metres to come to a stop at the final station. Find the time taken to travel between the two stations.

Q20:

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.

Q21:

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/s^{2}. Find the time taken, in seconds, for the second body to catch up to the first.

Q22:

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 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?

Q23:

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.

Q24:

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/s^{2} until it stopped. Find the average velocity of the body during the whole trip.

Q25:

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 π£ .

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