Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
Use the idea of inertia to explain each of these.
Newton's first law. A body keeps its velocity (stays at rest, or moves in a straight line at a steady speed) unless a net force acts on it. This reluctance to change velocity is inertia, and mass measures it.
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. A body keeps its velocity unless a force acts on it. Find which part is forced to change, and which is not.
Step 1. (a) The brakes slow the bus and, through friction, the passengers' feet. The upper body has no such force and keeps moving forward, so the passengers lurch forward.
Step 2. (b) You swing the umbrella and stop it suddenly. The cloth stops; the drops are only loosely held, so they keep moving and fly off.
Step 3. (c) The cloth is pulled away so fast that friction acts on the plates for only a very short time. Their inertia keeps them almost at rest.
Answer: In each case one part is forced to change its motion, and the other part, by its inertia, keeps going (or keeps still).
Watch out. No forward force throws the passengers in (a). They simply keep the speed they already had.
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