A 4 kg mass moves under the influence of a force F = (4 t³ i -3 t j ) N where t is the time in second. If mass starts from origin at t=0 , the velocity and position after t=2 ~s will be:

Step-by-step solution

Given F = (4t^3 i - 3t j ) N, m = 4 kg a = F m = t^3 i - 3t 4 j Integrating with v (0) = 0 : v = t^4 4 i - 3t^2 8 j At t = 2 : v = 16 4 i - 12 8 j = 4 i - 3 2 j Integrating with r (0) = 0 : r = t^5 20 i - t^3 8 j At t = 2 : r = 32 20 i - 8 8 j = 8 5 i - j