Problem 1 In physics lab you set a 1 kg cart to rolling with a velocity of 1 m/s. It collides with another cart and after the collision this 1 kg cart has a speed of 0 m/s. The collision lasted for exactly 0.5 seconds. The force probe on the cart allows you to measure the force of the collision, but is an uncalibrated force probe, so the function you have is with an unknown constant, A. The function is: F(t) = A[2t - 4t2] for the time interval 0 St 0.5 s A. (5 points) Use calculus to find the impulse, J, acting on the 1 kg cart during the collision, in terms of the unknown constant, A. Do not include units in your answer so it is easier to use in future steps. B. (5 points) Find the change in momentum that the 1 kg cart experienced during the collision. Include units in this numeric answer. C. (5 points) Find the numeric value of the constant, A. Do not include units in this answer. Problem 2 You suspend a spring from a support rod and hang a mass from the bottom of the spring. You set it in motion, and measure the velocity as a function of time to be: V(t) = -0.8 - sin (6- m t) A. (5 points) Use calculus to find the function for the acceleration as a function of time for this motion, where time is the only unknown, and correct units are included where appropriate. B. (10 points) Use calculus to find the function for the position as a function of time for this motion, where time is the only unknown, and correct units are included where appropriate