Terminal velocity and variable acceleration

Acceleration is seldom constant over long periods of time. In the next chapter we see that acceleration results from forces. In free fall, the force from air resistance gets large above about 10 m/s for falling objects such as balls. Air resistance dominates the motion of light objects with large surfaces—such as a sheet of paper. A flat sheet of paper falls slowly whereas a crumpled sheet falls quickly because of the relative strength of air resistance forces compared to gravity. Read the text aloud
The graph below shows the air speed of a parachute jumper who jumps out of a plane and falls freely for 28 s. At 28 s she opens her parachute. The vertical axis is speed (in meters per second) and the horizontal axis is time. Can you tell from the graph which part of the motion is accelerated and which is not? Read the text aloud
Speed vs. time graph for a skydiver
For the first few seconds, before the parachute has opened, the jumper is in free fall with an acceleration of g (A). Notice that after a few seconds the graph curves, becoming more horizontal (B). That is because the force of air resistance increases quickly with speed. Right around 70 m/s (C) the force of air resistance equals the force of gravity and acceleration is reduced to zero. For this skydiver, 70 m/s is her terminal velocity, the constant speed she reaches when air resistance reduces acceleration to zero. Read the text aloud
An open parachute greatly increases air resistance and the jumper immediately slows down (D). She is still accelerated, but now the acceleration acts in a direction opposite to her velocity. Notice that the downward curve of the v vs. t graph is very steep at D just after the parachute opens. This is because the upward force of air resistance on an open parachute at 70 m/s is much greater than the downward force of gravity on the jumper. The area and shape of the parachute is designed to produce a safe terminal velocity of about 5 m/s (E) for a normal skydiver’s weight. Read the text aloud
When an object falls in a medium—whether it is the air in the atmosphere or water in the ocean—it will reach a terminal velocity. How fast it reaches terminal velocity and the value of that terminal velocity depends on properties of the medium (air or water) and the shape of the falling object. When designing a spacecraft to re-enter the Earth’s atmosphere, or an oil drilling device that will be lowered to the ocean floor, the terminal velocity of the medium is an important consideration. Read the text aloud

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