Given that the acceleration vector is a(t)=(−1cos(−t),−1sin(−t),2t)a(t)=( −1cos⁡(−t),−1sin⁡(−t),2t), the initial velocity is v(0)=(1,0,1)v(0)=(1,0,1), and the initial position vector is r(0)=(1,1,1)r(0)=(1,1,1), Compute:a. The Velocity Vector v(t): _ i + _ j +_kb. The position vector r(t): _i + _ j + _k

(a) assume the equation x = at^3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.) (b) determine the dimensions of the derivative dx/dt = 3at^2 + b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)