At time t=0
an object (mass m
) starts being pushed towards the positive x-direction with a force F
. A different force directly proportional to the velocity v
of the object (magnitude k
v
, where k
is some positive constant), points to the negative x-direction, resisting the movement of the object.
According to Newton's 2nd law, the total force is equal to the mass m
times acceleration a
. Using Newton's 2nd law and the fact that acceleration is the rate of change (time derivative) of velocity, formulate a differential equation from which you can solve the velocity v(t)
of the object at any time t
, and solve the equation with the initial condition v(0)=u
.
v(t)=
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