If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph?

Solution

Physics sir · 4 steps

Acceleration is the slope of the v-t graph, and each straight piece of AMB has one fixed slope.

1. What to read. Acceleration is a = dv/dt, the slope of the velocity-time graph. Read the slope of the graph, not its height.
2. Part AM. From A to M the line is straight and going down. Its slope is constant and negative, so a is a flat line below the time axis for this whole part. The velocity crossing zero halfway does not change the slope.
3. Part MB. From M to B the line is straight and going up. Its slope is constant and positive, so a is a flat line above the time axis. AM and MB each take two time divisions and change v by the same amount, so both levels have the same size.
4. So. The a-t graph is a constant negative value that jumps once, at M, to an equal constant positive value. That is option (c).

The idea to keep. Straight line on a v-t graph means constant acceleration, a flat line on the a-t graph. The acceleration changes only where the slope of the v-t graph changes, not where v crosses zero.

Answer from the NTA final answer key. Solution by PrepWiser.