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  4. The graph shown in figure shows the velocity v versus time t for a body. Which of the graphs shown in figure represents the corresponding acceleration versus time graph?

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Q. The graph shown in figure shows the velocity $v$ versus time $t$ for a body. Which of the graphs shown in figure represents the corresponding acceleration versus time graph?Physics Question Image

Motion in a Straight Line

Solution:

The slope of $v-t$ graph is acceleration, as $a=\frac{d v}{d t}$
The $v$ -t graph has a constant negative slope in the first half, it means acceleration is constant and negative in the first half.
In the second half the graph has a constant positive slope in the $v-t$ graph. Hence the acceleration is constant and positive in the second half.