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(D) The velocity-time graph is obtained by integrating the acceleration-time graph,as $v = \int a \, dt$.$1$. From $0$ to $t_{1}$,acceleration $a$ is

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(D) The velocity-time graph is obtained by integrating the acceleration-time graph,as $v = \int a \, dt$.$1$. From $0$ to $t_{1}$,acceleration $a$ is constant and positive. Therefore,the velocity increases linearly with time (a straight line with a positive slope).$2$. From $t_{1}$ to $t_{2}$,acceleration $a = 0$. Therefore,the velocity remains constant (a horizontal line).$3$. From $t_{2}$ to $t_{3}$,acceleration $a$ is constant and positive again. Therefore,the velocity increases linearly with time (a straight line with a positive slope).Comparing this behavior with the given options,the graph shown in $823-$d272 correctly represents this motion.

$(1)$ Velocity decreases	$(a)$ Linear graph (constant slope)
$(2)$ Velocity increases	$(b)$ Concave up graph (increasing slope)
$(3)$ Velocity is constant	$(c)$ Concave down graph (decreasing slope)

The acceleration-time graph for a body is shown in the graph. Which of the following graphs would probably represent the velocity of the body plotted against time?

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