PHYSICS · Multi-part · AP · Physics C: Mechanics · Work Energy and Power · Work Energy and Power
Problem
A particle of mass m moves along the positive x–axis. Its velocity varies with time according to v=bt2, where b is a positive constant. During the motion the particle is acted upon by a force F=at directed along +x, a being a constant.
(a) Obtain an expression for the instantaneous power delivered by the force as a function of time.
(b) Using your result from part (a), find the total work done by the force during the interval 0≤t≤T by integrating the power over time.
(c) Evaluate the work again by computing W=∫0TFdx directly and show that it equals the result obtained in part (b).