Question

Velocity of a body moving along a straight line with uniform acceleration $\left(a\right)$ reduces by $\frac{3}{4}$ of its initial velocity in time $t_0$. The total time of motion of the body till its velocity becomes zero is

• A. $\frac{4}{3}{t}_0$
• B. $\frac{3}{2}{t}_0$
• C. $\frac{5}{3}{t}_0$
• D. $\frac{8}{3}{t}_0$

Answer 1

The correct option is A $\frac{4}{3}{t}_0$

Given,

Velocity reduce by $\frac{3}{4}$ of initial.

Apply kinematic equation

$V=U+at$

$(v-\frac{3v}{4})=v+a{t}_o$

$a=\frac{0.25v-v}{t_o}=\frac{-0.75v}{t_o}......\left(1\right)$

For final velocity to be zero

$V=U+at$

$0=v+at$

$t=\frac{-v}{a}=\frac{-v}{\frac{-0.75v}{t_o}}=\frac{4}{3}{t}_o$

Time required to stop is $\frac{4}{3}{t}_o$.