A car accelerates from rest at a constant rate `alpha` for some time, after which it decelerates at a constant rate `beta,` to come to rest. If the total time elapsed is t seconds. Then evalute (a) the maximum velocity reached and (b) the total distance travelled.

Explanation

The total distance covered by the car during acceleration and retardation `s= s_(1)+s_(2), s_(1)= v^(2)"/"2a_(1)`
`s_(2)= v^(2)"/"2a_(2) " "s= (v^(2)"/"2a_(2))= v^(2)xx (a_(1)+a_(2))"/"2a_(1)a_(2)= a_(1)a_(2)t^(2)"/"2(a_(1)+a_(2))`.