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

(a) We have tan `theta_1=alpha` and tan `theta_2=beta`
If the car accelerates for `t_1`and decelerates for `t_2`then `t_1`=`t_2`
`t_1=(V_(max))/(alpha)`,`t_2=(V_(max))/(beta)`
Where `v_(max)` is the Maximum velocity of the car
`(1)/(alpha)+(1)/(beta)=(t_1+t_2)/(V_(max)`
or `V_(max)=(alphabetat)/(alpha+beta)`
(b)Distance covered in time t is the area under the curve
`s=(1)/(2)(V_(max))t=(alphabetat^(2))/(2(alpha+beta))`