Question

A body starts slipping down an incline and moves half meter in half second. How long will it take to move the next half meter?

Answer 1

Let its acceleration be $a$.

For first half-meter-

$u=0$ $t=0.5s$

$s=\frac{1}{2}a{t}^2$

$⟹0.5=\frac{1}{2}a\times {0.5}^2$

$⟹a=4m/s^2$

Now let at $t=t$ it completes another half meter and hence total distance is 1m. This also includes time taken to cover first half meter.

$s=\frac{1}{2}a{t}^2$

$⟹1=\frac{1}{2}4t^2$

$⟹t=\frac{1}{\sqrt{2}}=0.707s$

Hence time to cover next half meter only$=0.707s-0.5s$

$=0.207s$