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Question 1:

A rocket sled has the following equation of motion: 6vdot = 2700 - 24*v. How long must the rock fire before the sled travels 2000 m? The sled starts from rest.

I took the integral which of that equation which gamve me v(t) = 2700*t - 24*x. At rest v = 0. So 0 = 2700t - 24*(2000)

Solve for t and you get t = 17.78 seconds.

Does this look right? If not please let me know.

Question 2:

For each of the following models, obtain the free response and time constants if any.

16*xdot + 14*x = 0, x(0) = 6

I changed it to v's, which gave me 16*v + 14*vdot = 0, v(0) = 6

For time constant its c/m so tau = 14/16 = .875

Then for the free response its v(t) = v(0)*e^-t/tau

So for my final answer, v(t) = 6*e^-1.143*t

If there are any problems with this, can you please let me know where.

I just want to make sure Im doing this right.