Suppose that the graph of force vs. time for a very unusual spring has only straight lines. The cart hits the spring at t = 3.00 s, so force F = 0 up to that point. Then, after t = 3.00 s, the force increases linearly until it reaches a maximum at Fmax = 6.74 N at time t = 3.55 s. Then the spring pushes the cart away, and the force decreases linearly until it goes back to F = 0 at time t = 3.85 s.
a) Find the magnitude of the impulse exerted by the spring on the cart.
b) Find the speed of the cart just as it leaves the spring.
HINT: Assume the cart is at rest when the force exerted by the spring is a maximum.