A piece of stone is thrown vertically upwards. It reaches the maximum height in 3 seconds. If the acceleration of the stone be $9.8\ m/s^2$ directed towards the ground, calculate the initial velocity of the stone with which it is thrown upwards.

Here given, time taken to reach the maximum height $t=3\ s$

Final velocity $v=0$   [At the maximum height velocity is zero]

Gravitational acceleration $g=9.8\ m/s^2$

Let $u$ be the initial velocity of the stone.

On using the equation of motion $v=u+gt$

$0=u+(-9.8)\times3$   [Here stone is thrown upward, so $g$ is negtive]

Or $u=29.4\ m/s$

Therefore, the initial velocity with which the stone is thrown is $29.4\ m/s$.