The potential energy of a particle of mass 1 kg moving in the x-y plane is given by U = 3x + 4y (in joules), where x and y are in metres. The particle starts from rest at the point (6, 4) at t = 0. Which of the following statements is/are correct?

The particle has constant acceleration
The particle has zero acceleration
The speed of the particle when it crosses the y-axis is 10 m/s
The coordinates of the particle at t = 1 s are (4.5, 2)

Correct answer: The particle has constant acceleration

Solution

Since U is a linear function of x and y, its gradient is constant, giving a constant force and therefore constant acceleration. Using kinematics, the speed when x = 0 can be found from energy conservation.

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