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Question
A ball is dropped and its displacement vs time graph is as shown figure (displacement x is from ground and all quantities are +ve upwards).
- Plot qualitatively velocity vs time graph.
- Plot qualitatively acceleration vs time graph.
Solution
To calculate velocity we will find the slope which is calculated by `(dx)/(dt)` for the displacement-time curve and to find acceleration we will find slope `(dV)/(dt)` of the velocity-time curve.
Sign convention: We are taking downward as negative and upward as positive.
The ball is bouncing on the ground and it is clear from the graph that displacement x is positive throughout. The ball is dropped from a height and its velocity increases in a downward direction due to gravity pull. In this condition v is negative but the acceleration of the ball is equal to the acceleration due to gravity i.e, a = – g. When the ball rebounds in the upward direction its velocity is positive but acceleration is a = – g.
a. The velocity-time graph of the ball is shown in figure.
b. The acceleration-time graph of the ball os shown in figure.
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