Acceleration

After the air resistance becomes large enough to balance out a skydiver’s weight, they will have no net force. From Newton's First Law we already know that an object’s inertia prevents a change in velocity unless it experience a net force, so from that point when the forces are balanced and onward, the skydiver continues at a constant velocity until they open their parachute.

During the initial part of a skydive, before the drag force is large enough to balance out the weight,  there is a net force so their velocity changes.  The rate at which the velocity changes is known as the acceleration. Note that students often confuse velocity and acceleration because they are both rates of change, so to be specific: velocity defines the rate at which the position is changing and acceleration defines the rate at which the velocity is changing.  We can calculate the average acceleration (a) during a certain time interval (Δt) by subtracting the initial velocity (v_i) from the final velocity (v_f) to get the change in velocity (Δv) and then dividing by the time interval (Δt):

(1)  

Acceleration Direction

The direction of acceleration depends on the direction of the change in velocity. If the velocity becomes more negative, then acceleration must be negative. This is the case for our skydiver during the first part of the jump; their speed is increasing in the negative direction, so their velocity is becoming more negative and therefore acceleration is negative. Conversely, if an object moves in the negative direction, but slows down, the acceleration is positive, even though the velocity is still negative! This was the case for our skydiver just after opening their parachute, when they still moved downward, but were slowing down. Slowing down in the negative direction means the velocity is becoming less negative, so the acceleration must be positive. All of the possible combinations of velocity direction and speed change and the resulting acceleration are summarized in the following chart: