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Homework Statement
Car Dynamics
f(t)→ [itex]\frac{\frac{1}{M}}{s+\frac{D}{M}}[/itex]→y(t)
Applied Force Velocity
Homework 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.
The Attempt at a Solution
The first order Differential equation is y'(t)+[itex]\frac{D}{M}[/itex]y(t)=[itex]\frac{1}{M}[/itex]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.
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