A force of 20. Newtons to the left exerted on a cart for 10. Seconds. For what period of time must a 50.-newton force to the right act to produce an impulse of equal magnitude on the cart?

Impulse = (force) x (time)

The first impulse was (20 N) x (10 sec) = 200 meters/sec

The second one is (50 N) x (time) and we want it equal to the first one, so

(50 N) x (time) = 200 meters/sec

Divide each side by 50N : Time = 200/50 = 4 seconds

By the way, the quantity we're playing with here is the cart's momentum.