Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
The graph shows the force along the path of a trolley. The force rises in a straight line from to over the first , stays at from to , and falls to at .
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. The work is the area under the graph; then the work-energy theorem.
Step 1. Area. .
Step 2. Speed. , so .
Answer: (a) . (b) .
Check. The trapezium's area is also . Same.
Watch out. Multiplying the largest force by the whole distance, , counts area that is not under the graph.
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The work of a force that changes along the path is the area under its force-position graph, . For a spring, .
Kinetic energy is . The work-energy theorem: the net work done on a body equals its change in kinetic energy, .