Chapter 4, Problem 2STP

To determine

To choose: The correct option.

Answer to Problem 2STP

The correct option is (B), 20 m.

Explanation of Solution

Given:

The acceleration is $2.5\text{m}/{\text{s}}^2$ and time of travel of a sprinter is 4 s.Also, the sprinter starts from rest.

Formula used:

The position of any object moving with a constant acceleration can be expressed in terms of initial position $d_i$ , initial velocity $v_i$ and acceleration $a$ as,

  $d=d_i+v_i{t}_f+\frac{1}{2}a{t}_f^2$

Here $t_f$ represents the final time.

Calculation:

Since the sprinter starts from rest, so his initial position and velocity are zero.

Thus the final position or thus the distance travelled is given by

  $d=\frac{1}{2}a{t}_f^2$

Substituting the given value of acceleration and the time taken, the distance travelled is given by,

  $\begin{array}{c}d=\frac{1}{2}\times 2.5\left(4^2\right)\\ =20\text{ m}\end{array}$

Conclusion:

Thus, the correct option representing the distance travelled by the sprinter is (B), 20 m.