1. The problem statement, all variables and given/known data A 4.00-kg particle moves along the x axis. Its position varies with time according to x = t + 2.0t^3, where x is in meters and t is in seconds. Find (a) the kinetic energy of the particle at any time t, (b) the acceleration of the particle and the force acting on it at time t, and (c) the work done on the particle in the interval t = 0 to t = 2.00 s. 2. Relevant equations K.E. = 1/2 m v^2 = 2 + 24t^2 + 72t^4 acceleration = 12t force = 48t 3. The attempt at a solution I got the answers as you can see for part a and b, and i actually got the right answer eventually for part c as well using W = ΔK.E....however, the first time i tried getting the work i used the formula W = ∫F dot dx, evaluated from 0 to 2. which lead me to: 48t (t + 2t^3) from 0 to 2 which gave me the answer W = 1728 J, but that is not the same answer i got for W = ΔK.E. and i can't figure out why using the force to find work did not yield the right answer...any idea?