Say whether each claim is always true, sometimes true or never true, and give an example or a…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Say whether each claim is always true, sometimes true or never true, and give an example or a reason.
- The path length of a body can be less than the size of its displacement.
- A body can have a path length of and a displacement of zero.
- A body's average speed can be zero while its average velocity is not.
Need a reminder? The key ideaShow
Path length adds up every metre travelled, whatever the direction; it is never negative. Displacement is the change of position, with a sign:
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. Compare a straight line from start to end with the path actually taken.
Step 1. Claim (a). Never true. The displacement is the shortest way from start to end; any real path is at least as long. They are equal only when the body never turns back.
Step 2. Claim (b). Sometimes true: any trip that ends where it began. Four laps of a track end at the start, so the path length is and the displacement is zero.
Step 3. Claim (c). Never true. A zero average speed means a zero path length: the body never moved. Then its displacement, and its average velocity, are zero too.
Answer: (a) never; (b) sometimes, whenever the body ends where it began; (c) never.
Watch out. Average velocity can be zero while average speed is not, the other way round. Mixing up the two directions of this statement is the usual slip.
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