a body moving with uniform retardation covers 3km before the speed is reduced to half of its initial value. It comes to rest in another distance of how many metres?

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Retardation is uniform = a
let initial velocity = v
final velocity = v/2
distance travelled = 3 m
$$\begin{gathered} V^2-u^2 = 2as \\ \frac{v^2}{4} - v^2 = 2a\times 3 \\ -\frac{3v^2}{4} = 6a \\ a = \frac{-v^2}{8} km/s^2 \end{gathered}$$

Now in the second case
initial velocity = v/2
final velocity = 0
let distance travelled = x
$$\begin{gathered} we get \\ -\frac{v^2}{4} = 2ax \\ on substituting the value of a we get \\ x = 1 km \end{gathered}$$