17.A car accelerates from rest at a constant rate α for sometime and reaches a maximum velocity. Then at decelerates rate β to come to rest. If the time lapsed is ‘t’ ,then the maximum velocity acquired by the will be

solution:

The car starts from rest (u)=0

acceleration (a)=α

to reach maximum velocity “V₁“

then ,the car decelerates with (a)=-β

final velocity (V₂)=0

for the first case ,V₁=0+αt₁,t₁=V₁/α

for the second case, initial velocity(u)=V₁

with deceleration (a)=-β

final velocityV₂ =0

0=V₁-βt2

V₁=βt₂,t₂=V₁/β

Total time=V₁/α+V₁/β=V₁(β+α)/αβ=V₁=(αβ/α+β)t

V₁=(αβ/α+β)t