A safety bumper is placed at the end of a racetrack to stop out of control cars. The bumper is designed such that the force that the bumper applies to the car is a function of velocity (v) and displacement (x) of the front edge of the bumper. dv/dx = -Kv2(x + 1)3/dx
where K-30 s kg/m 5
m = 1500 kg
x varies from 0 to 3 meters
v(0) = 90 km/lh
Solve the ODE to calculate the velocity as a function of distance from the moment of impact (x-0) to full compression (x-3 m). Plot the results with appropriate axis labels.