Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A cage carries miners down a vertical shaft. At it is below ground level, and at it is below. It then comes back up and reaches below ground at .
Over a time :
Average speed is never negative; average velocity has the sign of the displacement.
Take ground level as and up as positive, so positions in the shaft are negative.
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.
Given. at , at , at .
Step 1. Going down. : downwards.
Step 2. The whole trip, velocity. .
Step 3. The whole trip, speed. Path length , so .
Answer: (a) . (b) and .
Check. Overall the cage ended lower than at , so a small negative average velocity makes sense.
Watch out. With up positive, "below ground" means negative. Forgetting the signs turns into , which would mean the cage went up.
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