A cart of mass is placed on a smooth horizontal track

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A cart of mass

1.5\,\text{kg}

is placed on a smooth horizontal track. A horizontal force acts on the cart whose magnitude depends on the displacement

x

(measured from the starting point) according to

F(x)=5x\,\text{N}

for

0\le x\le 2\,\text{m}

and becomes zero for

x>2\,\text{m}

. The cart starts from rest at

x=0

. (i) Calculate the work done by the force while the cart moves from

x=0

x=2\,\text{m}

. State the numerical value with proper units. (ii) Determine the speed of the cart at

x=2\,\text{m}

. (iii) Will the cart continue to move beyond

x=2\,\text{m}

? Give a brief reason for your answer.