Problem 3: (7 points) Jerk vector in polar coordinates Consider a particle moving in two dimensions, and use polar coordinates (r, () to describe its position. The velocity U = vr + vod and a = arr + ago in these coordinates is given in Taylor's book. In this problem, compute the jerk j = da/dt = d'F/dts, the change in the acceleration. More specifically write j = jrf + jog and determine j, and jo in terms of r, o, and up to three time derivatives of both r and o. [An aside: The jerk is not commonly used in physics courses, so the aim here to to make sure you understand and can generalize the computation of 7 and a . However, engineers often need to consider the jerk in designing things like elevators, cars, or roller coasters, because human balance often suffers under rapid changes in acceleration.]