A) \[\frac{{{\alpha }^{2}}\beta t}{{{\alpha }^{2}}+{{\beta }^{2}}}\]
B) \[\frac{\alpha \beta t}{\alpha +\beta }\]
C) \[\frac{{{\beta }^{2}}\alpha }{{{\alpha }^{2}}+\beta }\]
D) \[\frac{\alpha \beta }{t}\]
Correct Answer: B
Solution :
Let car accelerate for t second and attain a velocity v, it decelerates for (t - t) second and comes to rest. Then, from equation of motion, we have \[v=0+\alpha t\] \[0=v-\beta \,\,(t-t)\] or \[t=t-\frac{v}{\beta }\] But \[t=\frac{v}{\alpha }\] \[\therefore \] \[\frac{v}{\alpha }+\frac{v}{\beta }=t\] \[\Rightarrow \] \[v=\frac{\alpha \beta t}{\alpha +\beta }\]
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