Question

A runner makes one lap around a 200m of a circular track in a time of 25 s. The runner’s average speed is
A) $4\dfrac{m}{s}$
B) $0\dfrac{m}{s}$
C) $8\dfrac{m}{s}$
D) $16\pi \dfrac{m}{s}$

Answer 1

Hint: The average speed is defined as the ratio of the total distance travelled by the body to the total time taken whereas the average velocity is defined as the ratio of the total displacement of the body to the total time taken. If the initial and the final position of the body is the same then the average velocity of the body is zero as the displacement is zero.

Formula used:
The formula of the average speed is given by,
${v_{avg}} = \dfrac{{{s_t}}}{t}$
Where the average speed is ${v_{avg}}$ the total distance is ${s_t}$ and time taken is $t$.

Complete step by step answer:
It is given in the problem that the runner is running around a circular perimeter of 200 m in 25s.
The formula of the average speed is given by,
${v_{avg}} = \dfrac{{{s_t}}}{t}$
Where the average speed is ${v_{avg}}$ the total distance is ${s_t}$ and time taken is $t$.
Since the total distance travelled by the runner is 200 m and the time taken by the runner is $25s$.
The average speed is,
$ \Rightarrow {v_{avg}} = \dfrac{{{s_t}}}{t}$
$ \Rightarrow {v_{avg}} = \dfrac{{200}}{{25}}$
$ \Rightarrow {v_{avg}} = 8\dfrac{m}{s}$

The average speed of the runner is equal to ${v_{avg}} = 8\dfrac{m}{s}$. The correct answer for this problem is option C.

Note:
The students should understand and remember the formula of the average speed as it can be helpful in solving these kinds of problems. If in the problem the radius of the circular track is given then the students have to first take out the perimeter and then take the ratio with the time to get the average speed. It is important to convert the answer into the unit which is given in the options of the problem.