Terminal Velocity (OCR A Level Physics)

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Katie M

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Katie M

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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

Terminal Velocity diagram (1), downloadable AS & A Level Physics revision notes

Terminal Velocity diagram (2), downloadable AS & A Level Physics revision notes

Terminal Velocity diagram (3), downloadable AS & A Level Physics revision notes

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:

terminal-velocity-graph, IGCSE & GCSE Chemistry revision notes

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

Worked example

Skydivers jump out of a plane at intervals of a few seconds.

Skydivers A and B want to join up as they fall.

WE - Terminal velocity question image, downloadable AS & A Level Physics revision notes

If A is heavier than B, who should jump first?

  • Skydiver B should jump first since he will take less time to reach terminal velocity
    • His terminal velocity will also be a lower speed than that of skydiver A
  • This is because skydiver A has a higher mass, and hence, weight
    • A greater weight means a greater acceleration for A than B at every stage until terminal velocity
    • Air resistance gets larger with speed, so for air resistance to match A's weight, A must be travelling faster than at terminal velocity
  • This means if A were to jump first, skydiver B would never catch up
  • Skydiver B must jump first, then skydiver A can catch up

 

Worked example

The diagram below shows the graph of velocity v against time t for the ball as it travels through the oil. The ball enters the oil at time t = 0.Terminal Velocity Fluid Worked Example, downloadable AS & A Level Physics revision notesIn terms of the forces acting on the ball, describe and explain its motion at

a) Point A

b) Point 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

Examiner Tip

  • Exam questions about terminal velocity commonly involve the motion of skydivers as they fall
  • A common misconception is that skydivers move upwards when their parachutes are deployed - however, this is not the case, they are in fact decelerating to a lower terminal velocity

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Katie M

Author: Katie M

Expertise: Physics

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.