A car acceleartion from reat at a constant rate of ` 3ms^(-2) for sometime. Then it retards at constant tate of 6 ms^(-1)` and comes to rest. If the total tiem for which it remains in motion is ` 3` seconds. What is the total distance travelled ?

Options

A. (a) ` 3 m`
B. (b) ` 4.5 m`
C. (6 m`
D. (d) `9 .0`

Answer

D

Explanation

If ` a_1, a_2` = acceleration and retardatin fo the car while moving along a straight line path for timings ` t_1 ` and `t_2` and (t) is the velocity acquired by car after time ` t_1`).
` v= a_1 t_1 =a_2t_2` or `t_1 = a_2/a_1 xx t_2 = 6/3 t_2=2t_1`
But `t_1+t_2=3` or `2 t_2 +t_2 =3`
or ` t_2 =1 s`
hence `, t_1 =2 s, :. ` v=3 xx 2 = 6 m//s`
As ` S= ut + 1/2 at^2`
:. ` S_1 = 0 6 1 + 1/2 xx 3 xx2^2 = 6 m`
` S_2 =6 xx 1 + 1/2(-6) xx1^ = 6 -3 =3m`
:. ` S_1 + _2 = 6 +3 = 9m.