 For the third problem, we're going to consider a skydiver falling out of an aeroplane. First we draw a free body diagram, we have gravity acting downwards, and the drag force acting upwards. The drag force is a type of friction due to a fluid, in this case air, moving around an object. Unlike friction between solid objects, drag depends on the object's speed. This is something that you would have experienced. When you walk, you don't notice the air moving around you, but if you ride a bike, the air resistance is pretty obvious. For a small, slow-moving object, when the air moves smoothly past it, the drag is proportional to the speed of the object. But for a large, fast-moving object, the movement of the air around the object will be turbulent, and here the drag is proportional to the speed squared. A skydiver is large and fast-moving, so we can express the drag as fd equals cv squared, where v is the speed and c is a constant, which depends on things like the air density, the shape of the skydiver, and so on. We can apply Newton's second law to this case, so the sum of the forces is equal to ma. The sum of the forces here is mg downwards minus the drag force upwards. Now we're going to plot a graph of the speed versus time. So to start with, when the skydiver first jumps out of the aeroplane, the skydiver's speed is close to zero, and so the drag force is zero and the acceleration is just equal to g. You'll remember that on a speed time graph, a constant acceleration is a straight line. As the skydiver accelerates and the speed gets faster, the drag force increases, and the acceleration will decrease. This continues until the point where the drag force is equal to the gravitational force, and now the sum of forces is zero, and so the acceleration is zero, and the speed stops increasing. This point is called the terminal velocity. We can calculate the terminal velocity by setting a equal to zero and solving for v.