finding average speed
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.
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?
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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