If the speed of the F=4000 lb car is plotted over the 30-s time period. Find the variation of the traction force F needed to cause the motion from 20s to 30s.

1) 124.2 lb
2) 206.4 lb
3) 120 lb
4) 221 lb

From the graph for 0 < t < 20s:
v = (40/20)t = 2t ft/s
Differentiating equation with respect to time,  a =2 ft/s2.
For 20s < t < 30s:
v-40/t-20 = 50-40/30-20 and v = (t+20) ft/s
Differentiating equation with respect to time, a = 1 ft/s2.

Equation of motion:
For 0 < t < 20s from the graph :
S Fx = max and F20 = (4000/32.2)2 = 248.4 lb ------(1)
For 20 < t < 30s :
S Fx = max and F30= (4000/32.2)1 = 124.2 lb -------(2)

So, the traction force needed for the car to travel from 20s to 30s is 124.2 lb.