# Homework Help: Open Loop Response of a car using a Basic First Order Model

1. Jul 20, 2013

### ae4jm

1. The problem statement, all variables and given/known data
Car Dynamics

f(t)→ $\frac{\frac{1}{M}}{s+\frac{D}{M}}$→y(t)
Applied Force Velocity

2. Relevant equations
M=1,000 kg and D=1000 kg/s
Where f(t) represents the input force and y(t) is the output velocity. M is the Mass and D is the drag, both of which are assumed constant for each case to be considered.

3. The attempt at a solution
The first order Differential equation is y'(t)+$\frac{D}{M}$y(t)=$\frac{1}{M}$f(t)

After I got that I'm supposed to do: I get stuck below at b part. I appreciate any help.

b) Solve the differential equation for y(t) if the input is a step function scaled by the force F0, f(t)=F0u(t). The initial velocity y(0)=28.8m/s (75 km/hr). Choose F0 such that the final velocity is 100 km/hr (27.8 m/s).

c) Plot the velocity y(t) versus time. Your time axis should go from 0 to 100 sec. Label axes.

d) How does the velocity change if the drag, D, is reduced to 75 kg/s? Increased to 150 kg/s? Plot y(t) for both cases and compare to part b above.

Last edited: Jul 20, 2013
2. Jul 21, 2013

### rude man

This problem has just been posed by elijah78 and addressed by the savants of PF.