The velocity-time and acceleration-time graph | vedclass

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(B) From the given velocity-time graph,we observe that the velocity $v$ increases linearly with time $t$. This implies that the acceleration $a = \fra

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(B) From the given velocity-time graph,we observe that the velocity $v$ increases linearly with time $t$. This implies that the acceleration $a = \frac{dv}{dt}$ is constant and positive,which is consistent with the provided acceleration-time graph.Since $v = \frac{dx}{dt}$,and $v$ is a linear function of time (i.e.,$v = at + u$),the position $x$ is given by the integral of velocity with respect to time:$x = \int v \, dt = \int (at + u) \, dt = \frac{1}{2}at^2 + ut + x_0$This equation represents a parabola. Since the acceleration $a$ is positive,the position-time graph must be a parabola that opens upwards (concave up).Therefore,the correct graph is the one showing a parabolic increase in position with time.

The velocity-time and acceleration-time graphs of a particle are given. Its position-time graph may be given as:

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