Can someone please help me with this calculus physics problem?
v = −g τ + g τ e^( −t /τ )
where τ is a constant that depends on the size and shape of the body and on the viscosity of
the medium and e ≈ 2.718....
(a) Find the acceleration as a function of time.
(b) Show that for t → ∞, the speed approaches the terminal value −gτ.
(c) By differentiation, verify that the equation for the position as a function of time consistent with the above expression for the speed is
x=−gτt−gτ^2e−t/τ +gτ^2+x0. (d) What happens for small values of t?