Question

Heya, anyone who's good at Dynamics. I have a question involving kinetic friction. There's a box weighing 12 lb moving at a velocity of 4 ft/s on the ground when force F = (8t^2) lb is applied. Coefficient of kinetic friction is 0.2. It wants me to find the velocity at time equals 2 seconds. I've gone through it a couple of times and my answer keeps coming up as v = 163 ft/s. This is apparently wrong though, and I'm running out of attempts. Can someone help me? I'd be more than happy to tell you my methodology for the answer I've got.

Answer 1

Here's an illustration of te

Answer 2

The FBD I drew:



where N = normal force, W = weight, and f_k = kinetic friction