A motorcycle starts from rest at a traffic light and moves in a straight line. For the first 4.0 s it accelerates uniformly at 3.0 m/s2. It then continues at the speed it has reached for the next 6.0 s before the rider applies the brakes, producing a constant acceleration of –2.0 m/s2 until the motorcycle comes to rest.
Assume the motion is along the +x-axis with t=0 at the instant the light turns green and the initial position x=0 at the traffic light.
(a) Calculate the motorcycle’s speed at t=4.0s. Express your answer with appropriate units.
(b) Determine the displacement of the motorcycle during the first 4.0 s.
(c) Determine the displacement of the motorcycle during the interval from t=4.0s to t=10.0s.
(d) Calculate the time required for the motorcycle to come to rest after the brakes are applied at t=10.0s.
(e) Determine the displacement of the motorcycle during braking and the total displacement from t=0 until the motorcycle comes to rest.