ALC? An object of mass m is at rest in equilibrium at the origin. At t = 0 a new force is applied that has components where k1, k2, and k3 are constants. Calculate the position and velocity vectors as functions of time.

Solution 62CP Given that, F(t) = F (tx + F (t)y F(t) = k +1k 2y+ k 3…..(1) Mass of the object is m. Let, a be the acceleration. So, F(t) = ma ma = (k +1k 2y + k 3) a = (k + k + k t) m 1 2y 3 If we integrate the expression of a, we shall get the expression for velocity vector. Therefore, t adt = 1(k 1 k 2y+ k 3)dt 0m 1 t2 v(t) = mk t 1 k 2yt + k 32 ) + C At t = 0, v(t) = 0 So, C=0 2 Therefore, v(t) = (k t +1k 2yt + k 3t...