A bus drives along a straight highway for one hour and twenty minutes.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A bus drives along a straight highway for one hour and twenty minutes.
- It goes at for the first half of the time and at for the second half. What is its average speed?
- On another day it goes at for the first half of the distance and at for the second half. What is its average speed now?
Need a reminder? The key ideaShow
Over a time :
Average speed is never negative; average velocity has the sign of the displacement.
Equal times: the average speed is the mean of the two speeds. Equal distances: it is not; find the two times first.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Go back to the definition every time: total distance over total time.
Step 1. Equal times. In time at each speed, the bus covers in . Average: , the simple mean.
Step 2. Equal distances. Each half of length takes and hours, so the average is .
Answer: (a) . (b) .
Check. In (b) the bus spends more time at the slow speed, so the average is below the mean of . That is what we found.
Watch out. "Half the time" and "half the distance" sound alike but give different answers. The total time of the trip, given in the first line, is not needed at all.
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