A particle moves along the -axis under a force that varies with position according to…
PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power
Problem
A particle moves along the x-axis under a force that varies with position according to F(x)=kx2 newtons for 1≤x≤3, where k is a real constant. The work done by this force in moving the particle from x=1 to x=3 is 40 joules.
(a) Write, but do not evaluate, a definite integral that represents the work done by the force over the given interval.
(b) Evaluate the integral in part (a) in terms of k.
(c) Determine the value of k that yields 40 joules of work.