The velocity (meters/second) of an object at time t (seconds) is governed by the dif...

The velocity (meters/second) of an object at time t (seconds) is governed by the differential equation

(a) How is the velocity of the object changing at t = 0?

(b) Determine the value of the constant k.

(c) Determine the velocity of the object at time t.

(d) Is there a finite time t > 0 at which the object is at rest? Explain.

(e) What happens to the velocity of the object as t → ∞?