question_answer

A car starts from rest, moves with an acceleration a and then decelerates at a constant rate b for sometime to come to rest. If the total time taken is t. The maximum velocity of car is given by

A) \[\frac{abt}{(a+b)}\]

B)  \[\frac{{{a}^{2}}t}{a+b}\]

C)  \[\frac{at}{(a+b)}\]

D)  \[\frac{{{b}^{2}}t}{a+b}\]

Correct Answer: A

Solution :

 \[v=u+at\] \[t={{t}_{1}}+{{t}_{2}}\] \[{{t}_{2}}=t-{{t}_{1}}\] \[{{v}_{1}}=0+a{{t}_{1}}\] When car finally comes for rest v = 0 \[0=v-b(t-{{t}_{1}})\] \[\left( {{t}_{1}}=\frac{b}{a+b}{{t}_{1}}v=\frac{ab}{a+b}t \right)\]