Velocity of a body moving along a straight line with uniform acceleration (a) reduces by $\frac{3}{4}$ of its initial velocity in time t_o . The total time of motion of the body till its velocity becomes zero is

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$\frac{4}{3} t_{0}$

$\frac{3}{2} t_{\circ}$

$\frac{5}{3} t_{0}$

$\frac{8}{3} t_{\circ}$

answer is A.

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Detailed Solution

$\begin{array}{l} u - \frac{3 u}{4} = u - {at}_{0} \\ a = \frac{3 u}{4 t_{0}} (or) \frac{u}{a} = \frac{4}{3} t_{0} \end{array}$
Now, 0 = u – at (or) $t = \frac{u}{a} = \frac{4}{3} t_{o}$

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