A physics professor demonstrates his new "anti-gravity parachute" by exiting from a helicopter at an altitude of 1500 m with zero initial velocity. For 8 s he falls freely. Then he switches on the "parachute" and falls with a constant upward acceleration of 15 m/s² until h is downward speed reaches 5 m/s, whereupon he adjusts his controls to maintain that speed until he reaches the ground. 

(a) On a single graph, sketch his acceleration and velocity as functions of time. (Take upward to be positive.) 

(b) What is his speed at the end of the first 8 s? 

(c) For how long does he maintain the constant upward acceleration of 15 m/s²? 

(d) How far does he travel during the upward acceleration in part (c)? 

(e) How many seconds are required for the entire trip from the helicopter to the ground?