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 :
From equation of motion, we have \[v=u+at\] Since, body starts from rest\[u=0\]. Let\[{{t}_{1}}\]be time when body accelerates and\[{{t}_{2}}\]when it decelerates. \[\therefore \] \[t={{t}_{1}}+{{t}_{2}}\] \[\Rightarrow \] \[{{t}_{2}}=t-{{t}_{1}}\] \[\therefore \] \[v=0+a{{t}_{1}}\] ...(1) When, car finally comes to rest\[v=0\] \[\therefore \] \[0=v-b(t-{{t}_{1}})\] ...(2) From Eqs. (1) and (2), we get \[{{t}_{1}}=\frac{b}{a+b}t,v=\frac{ab}{a+b}t\]You need to login to perform this action.
You will be redirected in
3 sec