Question

If you observed a car traveling at a constant rate around a circular track of 100 m diameter in 5 seconds, what is it's rate of motion in m/s?
Then what would it be in miles/hour?

Answer 1

A circle of diameter d=100m has a radius of d/2=50m
As \[v=\omega R\] and \[\omega=2\pi f\] \[f=1/T\]
The period of the motion is the time taken for one circuit: T=5s
So.
\[v=\omega R =2\pi fR= 2\pi R/T = (100\pi)/5 = 62.8ms ^{-1}\]
which is 153 miles per hour.
pretty fast.

Answer 2

Thank-you, but I have one question. How come you didn't multiply the '2'?
This is very helpful, and I am getting the same answer, but I am confused as to why the 2 isn't multiplied.

Answer 3

The radius which is 100/2=50 but it is then multiplied by 2 again so goes back to 100. so 2R=100. does that help?

Answer 4

Yes, thank-you very much. You've been very helpful.