Question

The potential energy of a particle of mass 1 kg moving along x-axis given by U(x)= [ x^ 2/2 -x ]J. If total mechanical energy of particle is 2 J, then find its maximum speed.​

Answer 1

Answer:

2m/s.

Explanation:

Given that, $U(x)=\frac{x^{2}}{2} -x$

It is known that, maximum speed is achieved when the particle attains maximum kinetic energy i.e., minimum potntial energy(U).

Here, U(x) reaches minimum at x = 0 and the value of U(x) at x = 0 is 0J.

So, potential energy + kinetic energy = total mechanical energy.

  =>  $0+ \frac{1}{2}mv^{2}= 2$

  =>  $\frac{1}{2} (1)v^{2}=2$

  =>  $v^{2}=4$

  =>  v = maximum velocity achieved = 2 m/s.