Velocity of a body moving along a straight li | vedclass

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Question

(A) Let the initial velocity be $u$. The velocity reduces by $\frac{3}{4}u$ in time $t_0$,so the final velocity $v$ at time $t_0$ is $v = u - \frac{3}

Vedclass · Accepted Answer

$\frac{4}{3} t_0$

Vedclass · Answer

(A) Let the initial velocity be $u$. The velocity reduces by $\frac{3}{4}u$ in time $t_0$,so the final velocity $v$ at time $t_0$ is $v = u - \frac{3}{4}u = \frac{1}{4}u$.Using the first equation of motion,$v = u + at$,where acceleration is negative (retardation),we have $\frac{1}{4}u = u - at_0$.Rearranging gives $at_0 = u - \frac{1}{4}u = \frac{3}{4}u$,which implies $a = \frac{3u}{4t_0}$.Let $T$ be the total time taken for the velocity to become zero. Using $v = u - aT$ with $v = 0$,we get $0 = u - aT$,so $T = \frac{u}{a}$.Substituting the value of $a$,we get $T = \frac{u}{(3u / 4t_0)} = \frac{4}{3}t_0$.

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

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