Assume a tomato is in frictionless free fall with a downward velocity v increasing at a constant rate g (g is the gravitational constant). Suppose that the initial velocity is v0 and find a formula for v(t) in terms of

v0 and g.

b) Now introduce a negative term representing air friction that is proportional to the velocity (hence of the form -kv for some constant k). Now find a formula for v(t), Show that as t grows, the velocity approaches the terminal velocity $\displaystyle \frac{g}{k} $