finding average speed

Physics Tutorial

finding average speed

Intro

In situations where you are given different speeds and the average speed is required, you need to keep in mind that the average speed is by definition: total distance/time elapsed. People get this wrong all the time, trying to do s= (s1+s2+s3+.. )/(number of s’s). Be careful.

Sample Problem

John is in a hurry to meet his girlfriend. To catch the bus, he runs 1000 m in 200 s. The bus travels 25 km at a speed of 50 km/h. What was John’s average speed in m/s?

Solution

1) Use definition of average speed (s) in terms of total distance traveled (d) and time elapsed (t) s=d/t.
2) Since we have different speeds, we should use: d=d1+d2 and t=t1+t2
2) We are told: d1=1000 m, d2=25 km=25000 m.
3) Also t1= 200 s but we still have to figure out t2.
4) From s=d/t, we can use: t2=d2/s2 = 25km /(50 km/h) = 0.5 h = 30 min = 30×60 s =1800 s
5) Putting everything together: s= (d1+d2)/(t1+t2) = (1000m+25000m) / (200 s + 1800 s) = 26000 m /2000 s = 13 m/s.

* Had you used s= (s1+s2)/2 = (1000m/200s + 50km/h)/2 = (5m/s + 13.89m/s)/2 = 9.44 m/s, which is incorrect.



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