First slide

Conservative force a negative gradient of potential energy

Question

Potential energy of a particle along x-axis varies as shown in the figure. If the particle is released from rest at a point on x-axis.

Difficult

A

It will move in negative x-direction
B

It will move with constant acceleration
C

(v - x) graph for a particle is parabolic
D

All of these

Solution

$F = - \frac{dU}{dx}$ if slope is +Ve body will move in the negative X direction. Also, since the slope is constant acceleration is constant. Thus $\frac{dv}{dt}$ = constant and as a result $\frac{dv}{dx} \frac{dx}{dt}$ = constant. $\frac{dv}{dx} V$ = constant. On integrating, $\frac{V^{2}}{2}$ = X + C. Thus V² is $\propto$ X.

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