A stone is thrown in a vertically upward direction with a velocity of 5 m/s .If the acceleration of the stone during its motion is 10 m/$s^2$ in the downward direction, what will be the height attained by the stone and how much time will it take to reach there?

Step 1: Given

Initial velocity $u=5m/s$

Acceleration (in downward direction)(a= 10 m/$s^2$)

Final velocity $v=0$

Let t and h are height and time.

Step 2: Formula used

$v=u+at$ (From the first equation of motion)

$v^2=u^2+2ah$ (From the third equation of motion)

Step 3: Finding height

Putting all the values

$0=5^2-2\times 10\times h$

After solving

h = 1.25 m

Thus, the height attained by the stone is 1.25 m

Step 4: Finding time

$v=u+at$

Putting all the values

$0=5-10\times t$

After solving

t = 0.5 s

Hence, time taken to reach the maximum height is 0.5 seconds.