A force F (x) = (-5.0x2 + 7.0x) N acts on a particle. (a) How much work does the force do on the particle as it moves from x = 2.0 m to x = 5.0 m? (b) Picking a convenient reference point of the potential energy to be zero at x = co, find the potential energy for this force.

Part a)

Work done is given as

W = -121.5 J

Part b)

Potential energy of the system is given as

Explanation:

As we know that work done by variable force is given as

here we know that

so we have

so we have

here we displace it from x = 2 to x = 5

so we will have

Part b)

As we know that change in Potential energy = work done

the part of the wave he is travelling on is the crest