Question

An athlete starts running from rest. He accelerates uniformly and completes $100m$ race in $10s$. Find his acceleration.

Answer 1

Step 1 - Given:

Initial velocity $\left(u\right)=0m/s.$

Distance travelled $\left(s\right)=100m.$

Time taken $\left(t\right)=10s.$

Step 2 - Calculation of acceleration:

Acceleration is defined as the rate of change in velocity.

For uniformly accelerated body, distance and time relation is given by,

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

Where, $s$ = distance covered, $u$ = initial velocity, $t$ = time taken, and $a$ = acceleration.

Putting all the values we get,

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

$100=0\times t+\frac{1}{2}a{\left(10\right)}^2.$

$100=25a$.

$a=\frac{100}{25}=4m/s^2.$

Hence, the acceleration is $\mathbf{4}\mathit{m}\mathbf{/}{\mathit{s}}^{\mathbf{2}}\mathbf{.}$