The Below is a graph of Fx vs time The form of Fx is Fx ABt

The Below is a graph of F_x vs. time. The form of F_x is F_x = A+Bt^2. Complete the equation for Fx by determining A and B. What is the total impulse?

Solution

Fx = A + Bt^2

at t = 0 Fx = 100 N

Therefore A = 100 N

at t = 20 s   F x = 0

Therefore   0 = 100 - B*400

                B = 0.25

Fx = 100 - 0.25 * t^2

Total impulse = Area under the curve

                     = integration (100 - 0.25t^2) from 0 to 20 s

                     = 100 * 20 - 0.25 * 20^3 / 3   = 1333.33 Ns