A) \[\frac{ab}{a+b}t\,m{{s}^{-1}}\]
B) \[\frac{ab}{a-b}t\,m{{s}^{-1}}\]
C) \[\frac{2ab}{a+b}t\,m{{s}^{-1}}\]
D) \[\frac{2ab}{a-b}t\,m{{s}^{-1}}\]
Correct Answer: A
Solution :
When the body accelerates initial velocity u = 0 acceleration = a and time \[={{t}_{1}}\] then final velocity \[v=0+a\,{{t}_{1}}\] ... (i) Now, as the body decelerates initial velocity, = v deceleration = - b and time \[=(t-{{t}_{1}})\] [t = total time elapsed] final velocity here \[{{v}_{2}}=0\] Again \[0=v-b(t-{{t}_{1}})\] ... (ii) From Eqs. (i) and (ii), we get \[a{{t}_{1}}=b(t-{{t}_{1}})\] or \[(a+b){{t}_{1}}=bt\] \[\Rightarrow \] \[{{t}_{1}}=\frac{bt}{(a+b)}\] Substituting the value of \[{{t}_{1}}\] in Eq. (i), we get \[v=\frac{abt}{(a+b)}m{{s}^{-1}}\]You need to login to perform this action.
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