A 0.10kg cart on a frictionless track is subjected to a horizontal force that varies with time as follows:
• 0 to 2ms: force rises uniformly from 0 to F0.
• 2 to 4ms: force falls uniformly from F0 back to 0.
• 4 to 6ms: force remains constant at −50N.
After t=6ms the cart is observed to have the same speed and direction as it had at t=0.
a. Determine the value of the peak force F0. (Give your answer to the nearest newton.)