Question

A particle moves in one dimension in a conservative force field. The variation of potential energy with distance is as shown in the graph below. If the particle starts to move from rest from the point $A$. Then

• A. The speed is zero at the points $A$ and $E$
• B. The acceleration vanishes at the points $A,B,C,D,E$
• C. The acceleration vanishes at the points $B,C,D$
• D. The speed is maximum at the point $D$

Answer 1

Answer: (A), (C)

The correct options are
A The speed is zero at the points $A$ and $E$
C The acceleration vanishes at the points $B,C,D$

Relation between conservative force and potential energy
$F=-\frac{dV}{dx}$
As slope of given graph is zero$(\frac{dV}{dx}=0)$ at points $B,C,D.$
Force $F=-\frac{dV}{dx}=ma=0$.
Hence $a=0$ at these points.

Speed is maximum at $B$ as the potential energy is minimum at this point.