Question

A car accelerates from rest at a constant rate αfor some time after which it decelerates at a constant rate β to come to rest. the maximum velocity v reached if total time (t second) is given by, (A) v=tαβ/α-β (B) v=t[β^2/α-β] (C) v=t[α^2/α+β] (D) v=t[αβ/α-β]​

Answer 1

Answer:

$v=\frac{\alpha \beta t }{\alpha +\beta }$

Explanation:

Let time for which it accelerates be t'. Then time for which it decelerates will be t-t'.

v = u + at ⇒ v = αt' ⇒ βv - αβt' = 0                                                  (1)

v = u + at ⇒ 0 = v - β(t-t') ⇒ αβt' + αv - αβt = 0                              (2)

∴ (1) + (2) ⇒ βv + αv - αβt = 0

⇒ v(α + β) = αβt

⇒ $v=\frac{\alpha \beta t }{\alpha +\beta }$