Starting from rest, a scooter travels with a constant acceleration for a time t₁ , subsequently moves with a constant velocity for the next t₂ , and finally undergoes a constant deceleration for the next t₃ to come to rest. A 500 N man sitting on the scooter behind the driver manages to remain at rest with respect to the scooter without touching any other part. The force exerted by the seat on the man is

Step-by-step solution

During the time interval t₁ , the scooter accelerates with an acceleration a₁ . The forces acting on the man are his weight W = 500 N acting downwards and the force from the seat. Since the man is at rest relative to the scooter, he accelerates with a₁ . The force exerted by the seat has a vertical normal component N = 500 N to balance gravity and a horizontal frictional component f = m a₁ to provide the acceleration. The total force exerted by the seat is F₁ = N^2 + f^2 = 500^2 + (m a₁)^2 , which is greater than 5