When the motorcyclist is at A he increases his speed along the vertical circular parth at the rate of v = (0.3t)ft/s², where t is in seconds. If he starts from rest when he is at A, determine his velocity and acceleration when he reaches B.

A ball thrown vertically upward from the top of a building with an initial velocity of v_A = 35 ft/s. Determine (a) how high above the top of the building the ball will go before it stops at B, (b) the time t_AB it takes to reach its maximum height, and (c) the total time t_AC needed for it to reach the ground at C from the instant it is released.

A sled is traveling down along a curve which can be approximated by the parabola y = x². When point B on the runner is coincident with point A on the curve (x_A = 2m, y_A = 1 m), the speed if B is measured as v_B = 8 m/s and the increase in speed is dv_B/dt = 4 m/s². Determine the magnitude of the acceleration of point B at this instant.

The slotted link is pinned at O, and as a result of rotation it drives the peg P along the horizontal guide. Compute the magnitude of the velocity and acceleration of P along the horizontal guide. Compute the magnitudes of the velocity and acceleration of P as a function of if = (3t) rad, where t is measured in seconds.

The flight path of a jet aircraft as it takes off is defined by the parmetric equations x = 1.25 t² and y = 0.03 t³, where t is the time after take-off, measured in seconds, and x and y are given in meters. At t = 40 s (just before it starts to level off), determine at this instant (a) the horizontal distance it is from the airport, (b) its altitude, (c) its speed and (d) the magnitude of its acceleration.