An automobile starts from rest and accelerates unifomly for ` 30 second to a speed of ` 72 km h^(-1)`. It then moves with a uniform veocit and it is finally brought to rest in `50 m` with a constant retardation. If the total distance travelled is ` 950 m`, find the accleration, the retaradation and total time taken.

Explanation

Let the automobile be accelrated from (O) to (A) It moves with constant velocity from (A) to (B) and then moves with constant retardstion from (B) to ` C Fig. 2 (b) . 35 .`
Taking motin of automobile from (O) to (A) we have ltbRgt ` u=0, a=t, t=30 , v=72 km//h = 20 m//s` ,
` S=?`
.
As, ` a = ( v-u) / t = ( 20 - 0) /( 30) = 2/3 m//s^2`
` S= ut + 1/2 at^2 = 0 + 1/2 xx 2/3 xx 30 ^2 = 300 m`
i.e. ` OA = 300 m, so . AB = OC- ( OA+BC)`
` = 950 - ( 300 + 500 +500 ) = 600 m`.
Taking motion of automoble from (A) to (B) tiem taken `= 600 /200 = 30 s`
Taking motion of autombole from (B) to (c ), we have
` u = 20 m//s, v= 0, a= ? S= 50 , t= ?`
` t= ( v^2 - u^2) /a = (0- 20^2) /(-4) = 5 s`
:. Total time ` = 30 + 30 + 5 = 65 s`.