The potential energy of a particle of mass moving in the -plane is

PHYSICS · Multi correct · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

The potential energy of a particle of mass

5\text{ kg}

moving in the

xy

-plane is

U=(7x+24y)\text{ J}

, where

x

and

y

are in metres. Initially, at

t=0

, the particle is at the origin and has velocity

(8.6\hat{i}+23.2\hat{j})\text{ m s}^{-1}

. Then (1) The speed of the particle at

t=4\text{ s}

5\text{ m s}^{-1}

. (2) The magnitude of the acceleration of the particle is

5\text{ m s}^{-2}

. (3) The direction of motion initially is at right angles to the direction of acceleration. (4) The path of the particle is a circle.