The Starship Enterprise initially moving with speed vo hits an intergalctic metero shower and expreiences a deceleration force given by:(adsbygoogle = window.adsbygoogle || []).push({});

F = -b*e^([alpha]*v) where b and [alpha] are constants. The star ships mass is m.

a) Determine v(t).

b) Determine the time required for the Enterprise to stop.

c) Show that x(t) is given by: (a really ugly function I don't want to type)

I've solved it, however my x(t) function isn't like what is given. I certain that my math and physics is right. If someone could do the problem, I'm curious to know what you get.

For a)

Finding v(t)

F = -b*e^([alpha]*v) = m dv/dt

Solving for v(t) I get: ln[m/([alpha]*b*t)] + vo

b)

When the ship stops.

v(t) = 0 = ln[m/([alpha]*b*t)] + vo

t = 1/(b*[alpha])*m*e^(vo*[alpha])

c)

Find x(t):

v(t) = dx/dt = ln[m/([alpha]*b*t)] + vo

Solving for x(t) = t/[alpha]*{ln(m/([alpha]*b*t) + vo*t + 1} + xo

My teacher said this problem was difficult. However it seems very straight forward to me, unless I'm doing something completely wrong.

Thanks

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# The Starship Enterprise (variable acceleration problem)

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