(a) a particle of mass m has the position vector 1. r(t) in(t) +sint2ke3*, for t > 0. obtain the particle's velocity, speed and acceleration (b) a particle of mass m is acted on by a force 1 +t' initially, at t 0, the particle is at the origin and has velocity 2(0)i find the velocity and position of the particle subsequently. (10) (c) a particle of mass m 1 moves along the z-axis under a conservative force f(x) = 22-21, (i) starting with the equation of motion, derive the energy equation. (hint: (i) identify the potential energy v(x). assuming that x > 0, obtain the posi- (ii) find the total energy e knowing that the particle has velocity v -0 when rewrite d2r/dt2 using the chain rule.) tion of the minimum of v(x). plot v(x) for x0 (15) -1. describe the type of motion.