Question

A point particle of mass 0.5 kg is moving along the x-axis under a force described by the potential energy U shown below. It is projected towards the right from the origin with a speed v. What is the minimum value of v for which the particle will escape infinitely far away from the origin towards right?

• A. 2√2 m/s
• B. 2 m/s
• C. 4 m/s
• D. the particle will never escape

Answer 1

Answer: (C)

4 m/s

Answer 2

The total energy of the particle is conserved. For the particle to escape to infinity, its total energy must be at least equal to the maximum potential energy it encounters. The maximum potential energy for $x \ge 0$ is 4 J. The initial total energy is $\frac{1}{2}mv^2$. Thus, $\frac{1}{2}mv^2 \ge 4$. With $m=0.5$ kg, this gives $v \ge 4$ m/s.