What is the Average Velocity of a Race Car on a Circular Track?

[121910marj]

Hi guys, sorry because I am quite confused.

If a person runs a quartermile circular race track for 8 laps for 25.0 min, what is the average speed? What is the average velocity?
Does that mean that the average velocity is zero m/s? Because the runner ends on the point where he started?

Thanks for your patience in answering above question but it's a lot of help.

 

[Fr34k]

8(laps) * 1/4 mile/lap =2 miles
This is the distance he traveled, doesn't matter if its circular.

2miles/0.42h=0.833mph
This is the average speed. Whole distance divided by time he needed.

 

[121910marj]

Yes, thank you. But my concern is about the average velocity.. if the track is circular would that mean that average velocity is 0 m/s.

 

[Fr34k]

What if that 8 times quarter mile circular track would just be 2 mile long straight track?
Would average velocity in that case, with your understanding also be 0?
What if track is just one big circle, or figure 8? Or some random curve that is connected?

I think I know where are you getting the idea. Are you confused by formula for average velocity being the "displacement" in a time interval? Displacement here means the whole path, all 8 tracks is a displacement here, not just the start/end point (which is the same).

You can imagine it like this: You do one step, and measure the time for that step, and another and another and another. Your steps are so small they are straight, so by your definition you can calculate the average speed. Now add all the steps and divide by whole time and you get average speed.

It doesn't really matter where you start and stop your path. <v>=dx/dt small distances over a short period of time integrated(summed) gives you average speed.

 

[manojr]

Because the runner ends on the point where he started?

I see what you mean.
You are thinking about displacement. Velocity is distance/time, not displacement/time.

 

[Doc Al]

Yes, thank you. But my concern is about the average velocity.. if the track is circular would that mean that average velocity is 0 m/s.

Yes. The displacement is zero so the average velocity would be zero.

The standard physics definitions:
ave velocity: displacement/time
ave speed: distance/time

 

[NascentOxygen]

Yes, thank you. But my concern is about the average velocity.. if the track is circular would that mean that average velocity is 0 m/s.

At any point around the track he has an instantaneous (non-zero) velocity, but the average velocity is 0 because his nett displacement is 0.

 

[Fr34k]

Ah sorry for the confusion I caused, in my language velocity and speed mean the same and I immediately assumed you were talking bout speed. Vocabulary updated :)

Yes in this case average velocity is 0.

 

[121910marj]

Thank you very much for all your help. Especially, DocAI, the PF mentor & NascentOxygen.. Thanks so much!