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

Average velocity is 0.296 m/s.

Average speed is 4.0 m/s.

Step-by-step 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* n=400* 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* 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}=(160)/(540)=0.296\ m/s`

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

So, average speed =
`(D_T)/(t)=(2160)/(540)=4\ m/s`