A car starts moving rectilinearly first with acceleration `alpha=5 m s^(-2)` (the initial velocity is equal to zero), then uniformly, and finally, deceleration at the same rate `alpha` comea to a stop. The time of motion equals `t=25 s`. The average velocity during this time is equal to `
`=72 km h^(-1)` How long does the car move unitromly?

Explanation

Let `t` be the time up to which the car accelerates or decelerates. The maximum velocity attained in this duration is `5_(t)`, The time upto which car moves uniformly`=25-2t`. The velocity-tme graph of the motion of car is drawn as shown as shown in
.
Given the average velocity is whole time of motion
`v_(av)=(72xx5)/(18)=20 m s^(-1)`
The average velocity from the graph can obtained as
`v_(av)=(Total displacement )/(Total time)`
`20=((1)/(2)xx[25+(25-2t)]xx5t)]xx5t)/(25)`=((1)/(2)xx[50-2t)]xx5t)/(25)`
`200=50 t-2t^(2)`
`rArr t^(2)-25t+100=0`
`rArr (t-20) (t-5) =0 rArrt=5 s` or `20 s`
But `t=20 s` is not possible .
Hence, `t=5 s`
The time up to which car moves uniformly
`=25-2t=25- 2xx5=15 s`.