A cart of mass moves on a smooth

PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power

Problem

A cart of mass

3\,\text{kg}

moves on a smooth, horizontal track from

x = 0

x = 7\,\text{m}

. The horizontal force acting on the cart varies with position as described below: • It increases uniformly from

0\,\text{N}

x = 0

12\,\text{N}

x = 2\,\text{m}

. • It remains constant at

12\,\text{N}

for

2\,\text{m} < x \le 5\,\text{m}

. • It then decreases uniformly, becoming

-6\,\text{N}

x = 7\,\text{m}

. The cart starts from rest at the origin. (i) Write an algebraic expression for the force

F(x)

in each of the three regions of motion. (ii) Calculate the work done on the cart in each region and hence obtain the total work done up to

x = 7\,\text{m}

. (iii) Find the speed of the cart at

x = 7\,\text{m}

. (iv) Determine, with justification, whether the cart reverses its direction of motion at any point before reaching

x = 7\,\text{m}