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(C) The acceleration $a$ is defined as the rate of change of velocity with respect to time,given by $a = \frac{dv}{dt}$. This represents the slope of

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(C) The acceleration $a$ is defined as the rate of change of velocity with respect to time,given by $a = \frac{dv}{dt}$. This represents the slope of the $v-t$ graph.$1$. At the beginning $(t=0)$,the slope of the $v-t$ graph is zero,so $a=0$.$2$. As $t$ increases,the slope becomes negative and its magnitude increases,reaching a maximum negative value at the point of inflection (where the curve changes from concave down to concave up).$3$. At the point where the velocity $v$ crosses the $t$-axis,the slope is at its maximum negative value.$4$. As $t$ continues to increase,the slope remains negative but its magnitude decreases,approaching zero as the curve flattens out.Looking at the options,the graph that starts at $a=0$,becomes negative,reaches a minimum,and returns towards $0$ is represented by option $C$.

The graph shows the variation with time $t$ of velocity $v$ of an object moving along a straight line. The $a-t$ graph will be:

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