EQUATIONS OF MOTION
When an object moves along a straight line with uniform acceleration, it is possible to relate its velocity, acceleration during motion and the distance covered by it in a certain time interval by a set of equations known as the equations of motion. There are three such equations. These are:
where u is the initial velocity of the object which moves with uniform acceleration a for time t, v is the final velocity, and s is the distance travelled by the object in time t.
Eq. (1) describes the velocitytime relation and Eq. (2) represents the positiontime relation. Eq. (3), which represents the relation between the position and the velocity, can be obtained from Eqs. (1) and (2) by eliminating t. These three equations can be derived by graphical method.
Problems Based on Equations of Motion
Q.1. A car acquires a velocity of 72km/h in 10 seconds starting from rest. Find (a) the acceleration (b) the average velocity (c) the distance travelled in this time.
Q.2. A body is accelerating at a constant rate of 10m/s^{2}. If the body starts from rest, how much distance will it cover in 2 seconds?
Q.3. The length of minutes hand of a clock in 5 cm. Calculate its speed.
Q.4. An object undergoes an acceleration of 8m/s^{2} starting from rest. Find the distance travelled in 1 second.
Q.5. A moving train is brought to rest within 20 seconds by applying brakes. Find the initial velocity, if the retardation due to brakes is 2m/s^{2}.
Q.6. A scooter acquires a velocity of 36km/h in 10 seconds just after the start. Calculate the acceleration of the scoter.
Q.7. A racing car has uniform acceleration of 4m/s^{2}. What distance will it cover in 10 seconds after start?
Q.8. A car accelerates uniformly from 18km/h to 36 km/h in 5 seconds. Calculate (i) acceleration and (ii) the distance covered by the car in that time.
Q.9. A body starts to slide over a horizontal surface with an initial velocity of 0.5 m/s. Due to friction, its velocity decreases at the rate of 0.05 m/s^{2}. How much time will it take for the body to stop?
Q.10. A car increases its speed from 20 km/h to 50 km/h in 10 seconds. What is its acceleration?
Q.11. A ship is moving at a speed of 56km/h. One second later, it is moving at 58km/h. What is its acceleration?
Q.12. A train starting from the rest moves with a uniform acceleration of 0.2 m/s^{2} for 5 minutes. Calculate the speed acquired and the distance travelled in this time.
Q.13. A bus was moving with a speed of 54 km/h. On applying brakes, it stopped in 8 seconds. Calculate the acceleration and the distance travelled before stopping.
Q.14. A train starting from rest attains a velocity of 72 km/h in 5 minutes. Assuming that the acceleration is uniform, find (i) the acceleration and (ii) the distance travelled by the train for attaining this velocity.
Q.15. Calculate the speed of the tip of second’s hand of a watch of length 1.5 cm.
Q.16. A cyclist goes once round a circular track of diameter 105m in 5 minutes. Calculate his speed.
Q.17. A cyclist moving on a circular track of radius 50m complete revolution in 4 minutes. What is his (i) average speed (ii) average velocity in one full revolution?
Q.18. A car starts from rest and moves along the xaxis with constant acceleration 5m/s^{2} for 8 seconds. If it then continues with constant velocity, what distance will the car cover in 12 seconds since it started from the rest?
Q.19. A motor cycle moving with a speed of 5 m/s is subjected to an acceleration of 0.2 m/s^{2}. Calculate the speed of the motor cycle after 10 seconds and the distance travelled in this time.
Q.20. The brakes applied to a car produce an acceleration of 6 m/s^{2} in the opposite direction to the motion. If the car takes 2 seconds to stop after the application of brakes, calculate the distance it travels during this time.

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