Falling Bodies. In the simplest model of the motion of a fallingbody, the velocity increases in proportion to the increase in thetime that the body has been falling. If the velocity is given infeet per second, measurements show the constant of proportionalityis approximately
32. a) A ball is falling at a velocity of 40 feet/sec after 1second. How fast is it falling after 3 seconds?
b) Express the change in the ball’s velocity ∆v as a linearfunction of the change in time ∆t.
c) Express v as a linear function of t. The model can beexpanded to keep track of the distance that the body has fallen. Ifthe distance d is measured in feet, the units of d ′ are feet persecond; in fact, d ′ = v. So the model describing the motion of thebody is given by the rate equations d ′ = v feet per second; v ′ =32 feet per second per second.
d) At what rate is the distance increasing after 1 second? After2 seconds? After 3 seconds?
e) Is d a linear function of t? Explain your answer.
