Physics

Problem

A cart moves along a straight horizontal track of total length

5\,\text{m}

. • For the first

2\,\text{m}

, a constant horizontal force of

4\,\text{N}

acts in the direction of motion, and the cart travels at a uniform speed of

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

. • For the remaining

3\,\text{m}

, the horizontal force varies with displacement according to

F(x)=4+3(x-2)\;\text{N}

(with

x

in metres from the starting point) while the cart now travels at a uniform speed of

1.5\,\text{m\,s}^{-1}

. a. (i) Calculate the work done by the force in each segment and hence obtain the total work for the complete

5\,\text{m}

journey. b. (ii) Using the total time of travel, determine the average power delivered to the cart over the entire journey.