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A delivery van drives the first 24 km of a straight road at 48 km/h, and the next 24 km at 32 km/h…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A delivery van drives the first of a straight road at , and the next at in heavy traffic.
- What is its average speed for the ?
- The driver wants an average of . Keeping the first half the same, how fast must the second half be?
Need a reminder? The key ideaShow
Over a time :
Average speed is never negative; average velocity has the sign of the displacement.
For two equal distances at speeds and , the average speed is , never the simple mean.
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.
Step 1. Times. and .
Step 2. Average speed. .
Step 3. The target. An average of needs . The first half used , leaving for : .
Answer: (a) . (b) .
Check. The formula agrees.
Watch out. The simple mean, , is the trap: the slow half takes longer, so it counts for more.
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