Question

A car accelerates from rest at a constant rate α for some time after which it decelerates at a constant rate β and comes to rest. If total time elapsed is t, then maximum velocity acquired by car will be

(a) (α²-β²)t/αβ

(b) (α²+β²)t/αβ

(c) (α+β)t/αβ

(d) αβt/α+β

Answer 1

Correct option (d) αβt/α+β

Explanation:

Initial velocity (u) = 0; Acceleration in the

first phase = α; Deceleration in the second phase  = β

and total time = t

When car is accelerating then

final velocity (v) = u+αt = 0+αt₁

or t₁ =v/α and when car is decelerating,

then final velocity 0 = v - βt or t₂ = v/β.

Therefore total time (t) =t₁+t₂ = v/α +v/β