Question

A body moving with uniform retardation covers 3 km before its speed is reduced to half of its initial value come to rest in another distance of___

Answer 1

Retardation is uniform = a
let initial velocity = v
final velocity = $\frac{v}{2}$
distance travelled = 3m
$v^2-u^2$ = 2 a s
$\frac{v^2}{4}$ - $v^2$ = $2a\times 3$
$\frac{{-3v}^2}{4}$= 6a
a= $\frac{{-v}^2}{8}$ $\frac{km}{s^2}$
Now in the second case
Initial velocity = $\frac{v}{2}$
final velocity = 0
let distance travelled = x
we get $\frac{{-v}^2}{4}$ = 2a x on substituting the value of a we get x = 1 km