91影视

The acceleration of a body is defined as the rate of change of velocity of a body in a given amount of time. The acceleration is used to determine the increase and decrease in the speed of the body.

Given data.

The initial velocity of the sprinter was $v_1鈥�=鈥�0$as she was started from rest.

The final velocity of the sprinter is $v_2鈥�=鈥�9.00鈥�\frac{\mathrm{m}}{\mathrm{s}}$.

The time taken by the sprinter for this motion is $螖t鈥�=鈥�1.38鈥�\mathrm{s}$.

Rule.

You know that acceleration is

role="math" localid="1642765622603" $a鈥�=鈥�\frac{v_2鈥�-鈥�v_1}{螖t}鈥�\left(i\right)$.

(a)

Now, substituting all the values in equation (i),

$\begin{array}{c}a鈥�=鈥�\frac{9.00鈥�\frac{\mathrm{m}}{\mathrm{s}}鈥�-鈥�0}{1.38鈥�\mathrm{s}}\\ =鈥�6.52鈥�\frac{\mathrm{m}}{{\mathrm{s}}^2}\end{array}$

Therefore, the acceleration of the sprinter is $6.52鈥�\frac{\mathrm{m}}{{\mathrm{s}}^2}$.

(b)

Now, the value of the acceleration in the unit of $\frac{\mathrm{km}}{{\mathrm{h}}^2}$will be

$\begin{array}{c}6.52鈥�\frac{\mathrm{m}}{{\mathrm{s}}^2}鈥�=鈥�6.52鈥�\frac{\mathrm{m}}{{\mathrm{s}}^2}鈥�脳鈥�\frac{1鈥�\mathrm{km}}{1000鈥�\mathrm{m}}鈥�脳鈥�{\left(鈥�\frac{3600鈥�\mathrm{s}}{1鈥�\mathrm{h}}\right)}^2\\ =鈥�8.45鈥�脳鈥�{10}^4鈥�\frac{\mathrm{km}}{{\mathrm{h}}^2}\end{array}$.

Therefore, the acceleration of the sprinter is $8.45鈥�脳鈥�{10}^4鈥�\frac{\mathrm{km}}{{\mathrm{h}}^2}$.