Q.34 A graph of potential energy V (x) versus x is shown in the figure. A particle of energy E0 is executing motion in it. Draw graph of velocity and kinetic energy versus x for one complete cycle AFA.


Hint: Use total mechanical energy, E0=KE+V(x).

Step 1: Find KE at different points and plot KE versus x graph.
We know that           

Total ME = KE + PE

E0=KE+V(x)KE=E0V(x)

at point A

x=0,V(x)=E0

KE=E0E0=0

at point B 

V(x)<E0

KE>0(positive)

atpointsCandDV(x)=0KE=E0maximumatpointFV(x)=E0

Hence, KE = 0

The variation is shown in the diagram.

Step 2: Use KE=12mv2 and plot velocity vs x graph.

As,

KE=12mv2

 At A and F. where KE = 0 v = 0
At C and D, KE is maximum. Therefore, v is ± max.

At B, KE is but not maximum.
Therefore,             v is ± some value              (< max)
The variation is shown in the diagram.