Activity 7.1.3.
Shown below are two graphs depicting the velocity of falling objects. On the left is the velocity of a skydiver, while on the right is the velocity of a meteorite entering the Earth’s atmosphere.
(a)
Begin with the skydiver’s velocity and use the given graph at left to measure the rate of change \(dv/dt\) when the velocity is \(v=0.5, 1.0, 1.5, 2.0\text{,}\) and \(2.5\text{.}\) Plot your values on the axes provided below. You will want to think carefully about this: you are plotting the derivative \(dv/dt\) as a function of velocity.
(b)
Now do the same thing with the meteorite’s velocity: use the given graph at right above to measure the rate of change \(dv/dt\) when the velocity is \(v=3.5,4.0,4.5\text{,}\) and \(5.0\text{.}\) Plot your values on the same axes used in part (a).
(c)
You should find that all your points lie on a line. Write the equation of this line being careful to use proper notation for the quantities on the horizontal and vertical axes.
(d)
The relationship you just found is a differential equation. Write a complete sentence that explains its meaning.
(e)
By looking at the differential equation, determine the values of the velocity for which the velocity increases.
(f)
By looking at the differential equation, determine the values of the velocity for which the velocity decreases.
(g)
By looking at the differential equation, determine the values of the velocity for which the velocity remains constant.
