Question

an athlete runs 5.4 laps around a circular track that is 400.0 m long. If this takes 540 s, what is the average velocity of the athlete? What is the average speed of the athlete over the complete distance of the run?

Answer 1

Answer:

Average velocity is 0.296 m/s.

Average speed is 4.0  m/s.

Explanation:

Given:

Distance of the circular track is, $D=400.0\ m$

Number of laps ran is, $n=5.4$

Time taken for the run is, $t=540\ s$

Now, total distance covered in 5.4 laps = $D_T=D\times n=400\times 5.4=2160\ m$

Also, since the path is a circle, the final position of the athlete after 5.4 laps will be 0.4 of 400 m ahead of the starting point.

Distance covered in 0.4 laps is, $\textrm{Displacemet}=0.4\times 400=160\ m$

Therefore, the displacement of the athlete will be 160 m as the athlete is 160 m ahead of the starting point and displacement depends on the initial and final points only.

Now, average velocity is given as:

$v_{avg}=\frac{\textrm{Displacemet}}{t}=\frac{160}{540}=0.296\ m/s$

Average speed is the ratio of total distance covered to total time taken.

So, average speed = $\frac{D_T}{t}=\frac{2160}{540}=4\ m/s$