3.3.6 Terminal Velocity

• For a body in free fall, the only force acting is its weight and its acceleration g is only due to gravity.
• The drag force increases as the body accelerates
  • This increase in velocity means the drag force also increases

• Due to Newton’s Second Law, this means the resultant force and therefore acceleration decreases (recall F = ma)
• When the drag force is equal to the gravitational pull on the body, the body will no longer accelerate and will fall at a constant velocity
• This velocity is called the terminal velocity

A skydiver in freefall reaching terminal velocity

• The graph shows how the velocity of the skydiver varies with time
• Since the acceleration is equal to the gradient of a velocity-time graph, the acceleration decreases and eventually becomes zero when terminal velocity is reached
• After the skydiver deploys their parachute, they decelerate to a lower terminal velocity to reduce the impact on landing

• This is demonstrated by the graph below:

A graph showing the changes in speed of the skydiver throughout their entire journey in freefall

• Skydiver B should jump first since he will take longer to reach terminal velocity
• This is because skydiver A has a higher mass, and hence, weight
• More weight means higher acceleration and hence higher speed, therefore, A will reach terminal velocity faster than B

Part (a)

At A:

• • The drag force is greater than the weight of the ball
  • Therefore, the ball is decelerating

Part (b)

At B:

• • The drag force is equal to the weight
  • The ball has reached terminal velocity and is no longer decelerating