Question

A 2Kg object is moving the positive X direction at a speed of 4 m/s. At time t=0 it is struck by a bat with a variable force in the positive x direction given by f +4 -t^2 This force last until t= 2seconds and the ceases to act. what is the finalspeed of object.

Answer 1

Mass of object = 2kg initial speed at k = 0 implies u = 4m/s variable force F = 4 - t^2 ma = 4 - t^2 2a = 4 - t^2 a = 2 - t^2/2 dv/dt = 2 - t^2/2 integral_4^v dv = integral_0^2 [2 - t^2/2]dt implies [v - 4] = [2t - t^3/6]_0^2 implies v - 4 = 4 - 8/6 = 0 implies v - 4 = 4 - 4/3 implies v = 8 - 4/3 = 20/3 V = 20/3 = 6.67 m/s