At t =0, an object of mass m is at rest at x =0 on a horizontal, frictionless su

Question

At t=0, an object of mass m is at rest at x=0 on a horizontal, frictionless surface. Starting at t=0, a horizontal force Fx=F0et/T is exerted on the object.

Part A

Find an expression for the object's velocity at an arbitrary later time t.

Express your answer in terms of the variables F0, m, T, and t.

f0etTxm

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Part B

What is the object's velocity after a very long time has elapsed?

Express your answer in terms of the variables F0, m, and T.

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f0etTxm

Explanation / Answer

F = Fo*e^-t/T

acceleration a = F/m = (Fo/m)*e^-t/T

velocity = integration of a

v = C - (Fo/m)*T^e^-t/T

given at t = 0 the speed = v = 0

therfore

0 = C - (Fo*T/m)*^e^-(0/T)

0 = C - (T*Fo/m)

C = T*Fo/m

therfore

v = T*Fo/m - Fo*T/m*e^-(t/T) = (Fo*T/m)*(1-e^-(t/T)

part(B)

for t = infinity

v = Fo*T/m <<--answer

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