Calculating Velocity from Position-Time Graph | Simple Problem Solution

[Allura]

[PLAIN]http://lc.cit.jmu.edu/cgi-bin/plot.png?file=safavifn_jmu_1283993422_6827202_plot.data

1. A bicyclist has the position-versus-time graph as shown. What is the bicyclist's velocity (in m/s) at t = 5 seconds?



2. Since this is a simple velocity problem, I thought it would be v= 60 m/ 5s



3. My answer was 12m/s

I don't know what I'm doing wrong, could it be that I'm reading the graph wrong?

 

[rock.freak667]

velocity is the rate of change of displacement with time or v=ds/dt. So you need to find the gradient of that section from t= 0 to t=5. At what point does it cut the vertical axis? What position does t=5 correspond to?

 

[Allura]

So would it be (61-51)/5? Since t=0 is 51m and t=5 is 61m?

 

[rock.freak667]

Yes that looks correct to me.

 

[Allura]

Thanks.

How would I do something like t=37s?

 

[rock.freak667]

Thanks.

How would I do something like t=37s?

Then you'd need to consider the line segment between t=30 and t=40.

So get the position at t=37, that will be one point. Then get the position at any time between 30 to 40 (so t=31 for example). Then just use the same gradient formula you used before.

 

[Allura]

Yay, I got it.

Thank you!