A particle moves along the x-axis so that at any time t > 0, its acceleration is given by a(t) = ln(1 + 2^{t}). If the velocity of the particle is 2 at time t = 1, what is the velocity of the particle at time t - 2?
- I'm having a tough time getting the antiderivative for a(t)
Is an exact answer required? Because you can express the velocity as
.
Then
and the integral can be approximately evaluated using technology.
I don't think an exact answer in terms of a finite number of elementary functions is possible (although I may stand corrected on this).