Translate each of the following into the language of derivatives of distance with respect to time. For each part, sketch a plot of the car's position s against time t, and indicate the concavity.
(a) The speed of the car is proportional to the distance it has traveled.
(b) The car is speeding up.
(c) I didn't say the car was slowing down; I said its rate of in-crease in speed was slowing down.
(d) The car's speed is increasing 10 miles per hour every minute.
(e) The car is slowing very gently to a stop.
(f) The car always travels the same distance in equal time intervals.