In a dream, you find that you can run at superhuman speeds, but there is also a resistant force that reduces your speed by one-half for each second that passes. Assume that the laws of physics still hold in your dreamworld, and that your initial speed is 1000 m/s.

(a) Sketch a smooth function v(t) that gives your velocity.

(b) What is your average velocity over the first 10 s?