91影视

The velocity of a body is the vector quantity and has the same unit as that of speed. It is defined as the rate of change of displacement in unit time.

Given data.

The initial velocity of the car is $v_o鈥�=鈥�28鈥�\frac{\mathrm{m}}{\mathrm{s}}$.

The final speed of the car is $v鈥�=鈥�0$as it comes to rest.

The time taken to come to rest is $螖t鈥�=鈥�8.0鈥�\mathrm{s}$.

Assumption.

Let the acceleration be a.

Also, assume that it travels $螖x$distance in the given time.

Now, you know that

role="math" localid="1642836157076" $v鈥�=鈥�v_o鈥�+鈥�a鈥�螖t鈥�\left(i\right)$.

The second equation of motion is

role="math" localid="1642836200507" $v^2鈥�=鈥�v_o^2鈥�+鈥�2a鈥�螖x鈥�\left(ii\right)$.

Now, substituting the values in equation (i),

$\begin{array}{c}v鈥�=鈥�v_o鈥�+鈥�a鈥�螖t\\ 0鈥�=鈥�28鈥�\frac{\mathrm{m}}{\mathrm{s}}鈥�+\left(a鈥�脳鈥�8.0鈥�\mathrm{s}\right)\\ a鈥�=鈥�-鈥�3.50鈥�\frac{\mathrm{m}}{{\mathrm{s}}^2}\end{array}$

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

$\begin{array}{c}{v}^2鈥�=鈥�v_o^2鈥�+鈥�2a鈥�螖x\\ 0^2鈥�=鈥�{\left(28.0鈥�\frac{\mathrm{m}}{\mathrm{s}}\right)}^2鈥�+鈥�\left[2鈥�脳鈥�\left(-鈥�3.50鈥�\frac{\mathrm{m}}{{\mathrm{s}}^2}\right)鈥�脳鈥�螖x\right]\\ 7.00鈥�\frac{\mathrm{m}}{{\mathrm{s}}^2}鈥�脳鈥�螖x鈥�=鈥�{\left(28.0鈥�\frac{\mathrm{m}}{\mathrm{s}}\right)}^2\\ 螖x鈥�=鈥�112.0鈥�\mathrm{m}\end{array}$

Therefore, the car travels 112.0 m in the given time.