# Kinematics Equations Practice Problems

A bus is driven at a speed of 18 m/s. The bus driver notices a competitor's van at a bus stop 180 m ahead. The van's schedule states it will leave the bus stop after 16 seconds. The bus driver wishes to reach the bus stop as the van takes off. The driver has a response time of 2 s before applying brakes and decelerating uniformly. Determine the speed of the bus as it arrives at the bus stop while the van is taking off.

A car takes off and accelerates uniformly for the first 7.5 s to attain its peak speed. The car covers 1 km in 45 s. Determine the car's speed as it crosses the point marking 1 km.

Kinematics shows that if a motorcycle starts from rest and accelerates uniformly, the distance covered is proportional to the square of the change in time. In the first 3.0 seconds, a motorcycle covers 12 meters. Determine the distance covered by the motorcycle in the first 8 seconds.

A box sliding at a constant speed of 5.0 m/s on a frictionless surface enters a rough, concrete surface. When the box moves 3.0 meters on concrete, its speed drops to 4.0 m/s. Determine the magnitude of deceleration of the box on concrete.

A child is driving a remote-control car at a steady velocity of 3.0 m/s along a straight line. The maximum deceleration of this car is about 1.0 m/s^{2}. Calculate the shortest possible stopping distance if the remote control response time is 0.20 s.

During a workout, a sprinter initially at rest at point A accelerates for 5.0 s at a constant rate of 2.0 m/s^{2}. Afterward, the sprinter maintains a constant speed for 15 s before he decides to decelerate at a constant rate of 4.0 m/s^{2}. The sprinter stops at point B. Calculate the distance from A to B.

A race pilot driving at a speed of 35 m/s noticed the presence of a competitor's car crashing 100 m in front of him. The pilot applies a negative acceleration of 9 m/s^{2}. When the race car is totally at rest, determine the distance separating it from the crash. Suppose that a race pilot's typical reaction time is 0.2 seconds.

A motorcyclist riding at a constant speed of 60 km/h on the highway applies a constant acceleration for 2 km until he reaches a speed of 80 km/h. Determine the motorcycle's acceleration.

In order to test the reliability of an old aircraft, it is desirable to achieve the speed of Mach 10. If aircraft is accelerated with the constant acceleration of 5g, then what would be the distance travelled by the aircraft in this period of acceleration? (Use 331 m/s for the speed of sound in cold air.)

In a Formula 1 race, the racer wish to achieve a constant acceleration of 3 m/s^{2} in order to win the race. What is the shortest time in the racer can reach the speed of 300 km/h if it is starting from the rest?

A boy practicing baseball strikes the ball and it leaves with a speed of 100 m/s. The ball was in the contact with the bat for about 40 ms and starts from rest. If acceleration was constant, what was the ball's acceleration during the strike?

In a cricket match, a bowler releases the ball at a speed of 144 km /h. Initially, the bowler was at rest. Assume that the bowler applies constant acceleration to the ball while running over a 2.0-m distance holding the ball. What acceleration did he give the ball?

A bullet-shaped ride in an amusement park weighs about 11000 pounds at its full capacity. From rest, it starts moving upwards from the ground. For safety purposes, it needs to be slow at first, and it takes 10.0 s to reach 8 m/s. At the end of 2.00 min, its speed is 40 m/s. Calculate the average acceleration of the ride

(i) during the first 10.0 s and

(ii) between 10.0 s and the end of 2.00 min.

Ride-O is testing its new product which is a mini-car that is designed for kids. The test aims to study the changes in the velocities of the mini-car at a 5-s interval. What is the average acceleration in each of the following intervals? Consider the convention that the east direction is positive.

(i) At the start of the interval, the mini-car is moving 1.5 m/s to the east, and at the end, it is moving to the east at 1.2 m/s.

(ii) At the start of the interval, the mini-car is moving due west at 1.75 m/s, and at the end, it is moving at 2.0 m/s, still towards the west.

(iii) At the start, the mini-car is moving to the east at 1.9 m/s, and at the end, it is moving to the west at 1.9 m/s.

A cheetah chasing a deer travels the distance between two poles 100 m away from each other within 10 s. Its speed, as it passes the second pole, is 15 m/s. What was the speed of the cheetah at the first pole assuming the cheetah has uniform acceleration?

In a motorcycle race, a biker surprised by a cat applies the brakes, producing a negative acceleration of 4m/s2. If the biker was riding at an initial speed of 126 km/h (35 m/s). Calculate the distance covered by the biker before going to a complete stop.

A train, maintaining a steady speed of 120 km/h, initiates braking with a constant deceleration of 0.75 m/s^{2}. Determine the distance it covers within the initial and tenth seconds of deceleration

A car accelerates from a standstill to a speed of 25 m/s in a straight line on a highway. Estimate the average acceleration of the car during this acceleration phase. The car accelerates through a distance of approximately 150 m.

On a slippery icy surface, a sledge with a mass of 20 kg is in motion with a velocity of 5m/s due to a force of 70 N applied to it. Determine the magnitude of the distance covered by the sledge along the icy surface before it halts due to friction. The sledge's motion is affected by the kinetic friction, characterized by the coefficient 0.2.

A vessel, measuring 120 m in length, starts its uniform acceleration from a complete stop. When the front of the vessel reaches a buoy located 300 m away from its initial position, it is traveling at a speed of 12 m/s. What will be the speed of the rear end of the vessel as it passes the buoy?

Suppose a car is moving at a speed of 80 km/h, and in the event of a collision, it experiences a uniform deceleration of 40 g's (1.00 g = 9.80 m/s²). Calculate the distance over which the front end of the car must be designed to collapse to ensure passenger safety if the car comes to rest during the collision.