Question

if the velocity 'u' of a body moving in a straight line with a constant retardation'a' is reduced by 75% in time 't',ten what is the time?

Answer 1

See photo. I have explained everything there.

Answer 2

If the velocity 'u' of a body moving in a straight line with a constant retardation'a' is reduced by 75% in time 't'.

We have to find the time t.

initial velocity of a body = u

constant retardation acting on the body = -a [ negative sign indicates it is retardation ]

velocity of the body is reduced by 75 % in time t.

means, final velocity of body , v = u - 75 % of u

$=u-\frac{75u}{100}\\\\=u-\frac{3u}{4}\\\\=\frac{u}{4}$

now, using formula, v = u + at

$\implies\frac{u}{4}=u+(-at)\\\\\implies\frac{u}{4}-u=-at\\\\\implies\frac{-3u}{4}=-at\\\\\implies t=\frac{3u}{4a}$

Therefore the time taken by the body to reduce velocity by 75% is 3u/4a.