Question

Potential energy of the particle of mass 0.5 kg moving along x axis is
given by U= 2*x(x-3) , the speed of particle is maximum at
A )1 m
B)1.5 m
C) 2 m
D) 3 m

Answer 1

Given:

Potential Energy relation :

U = 2x(x - 3)

To find:

Max speed of object at which position?

Calculation:

$U = 2x(x - 3)$

$\implies \: U = 2 {x}^{2} - 6x$

• Now, differentiation w.r.t x :

$\implies \: f = - \dfrac{dU}{dx} = - 4x + 6$

$\implies \: a = \dfrac{6 - 4x }{0.5}$

$\implies \: a = 12 - 8x$

$\implies \: \dfrac{dv}{dt} = 12 - 8x$

• For max velocity, 1st order derivative must be zero.

$\implies \: \dfrac{dv}{dt} = 12 - 8x = 0$

$\implies \: 12 - 8x = 0$

$\implies \: 8x = 12$

$\implies \: x = 1.5 \: metres$

So, velocity is max when x = 1.5 metres.