A car of mass $$1000\,kg$$  is moving at a speed of $$30\,m/s.$$  Brakes are applied to bring the car to rest. If the deceleration is $$5\,m/{s^2}$$  the car comes to stop after travelling $$dm$$  in $$ts.$$ Then

Solution :
Given: mass of car $$m = 1000\,kg,u = 30\,m/s;v = 0\,m/s$$
retardation, $$ - a = 5\,m/{s^2}$$
By equation, $${v^2} - {u^2} = 2as$$
$$\eqalign{ & 0 - {\left( {30} \right)^2} = - 2 \times 5 \times d \cr & \therefore d = \frac{{900}}{{10}} = 90\,m \cr} $$
and $$a = \frac{{v - u}}{t}\therefore t = \frac{{v - u}}{a} = \frac{{0 - 30}}{{ - 5}} = 6s$$