A stone is thrown vertically upwards with an initial velocity of 45 m/s, then find the time taken by the stone to rise to its maximum height.

Given, 
Initial velocity, u = 45m/s
Final velocity, v = 0 (as the stone comes to rest on reaching the maximum height)
When a stone is thrown upward, a gravitational force acts on it which resists its motion in the upward direction. So, acceleration due to gravity acts on the stone in the opposite direction of its motion. 
Acceleration due to gravity, g = -10m/s²

The first equation of motion is: 

$v= u + gt$
Putting the given values in the above equation, we get,
$\Rightarrow 0=45+\left(-10\right)\times \mathrm{t}$
$\Rightarrow 45-10\mathrm{t}=0$
$\Rightarrow 10\mathrm{t}=45$
$\Rightarrow \mathrm{t}=\mathrm{ }\frac{45}{10}$
$\Rightarrow \mathrm{t}=4.5 \mathrm{s}$

A stone is thrown vertically upwards with an initial velocity of 45m/s, then the time taken by the stone to rise to its maximum height is 4.5s.