The velocity-displacement graph of a particle | vedclass

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(C) The equation of the given straight line in the $V-S$ graph is $V = -mS + V_0$,where $m$ is the magnitude of the slope and $V_0$ is the intercept.T

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The acceleration versus displacement graph is a straight line.

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(C) The equation of the given straight line in the $V-S$ graph is $V = -mS + V_0$,where $m$ is the magnitude of the slope and $V_0$ is the intercept.The slope of the graph is $\frac{dV}{dS} = -m$.We know that acceleration $a = V \left(\frac{dV}{dS}\right)$.Substituting the values,we get $a = (-mS + V_0)(-m)$.$a = m^2S - mV_0$.This equation is of the form $y = mx + c$,which represents a straight line. Therefore,the acceleration versus displacement graph is a straight line.

The velocity-displacement graph of a particle moving in a straight line is as shown in the figure.

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