Question

A car travels with a speed of 20m/s to east.at t=0,the driver sees a bus coming 100m behind with a speed of 25m/s breaks immediately and decelerates uniformly for 2s.After a time t after applying breaks,the bus passes the car and car travels with the same speed which it had. (Take the speed of car after deceleration as u)
1.write an expression for the deceleration of the car in terms of u and t
2.when the bus passes the car,write an expression for the distance travelled by car

Answer 1

The bus travels the distance

$$100+d=25t$$

The car travels the distance

$$d=\frac{20^2-u^2}{2a}$$

1)

$$a=\frac{20-u}{t}$$

2)

$$d=\frac{20^2-u^2}{2a}=t\frac{20^2-u^2}{2(20-a)}=\frac{20+u}{2}t$$

So,

$$d=\frac{20+u}{2}t$$