Non-uniform motion

AS Level Physics · Dynamics. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.

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The idea

Friction and drag are resistive forces. They always act against the motion. Friction acts between solid surfaces. Drag (including air resistance) acts on an object moving through a fluid, and it increases as the speed increases.

An object dropped from rest starts with acceleration g, because the drag is zero. As it speeds up, the drag grows, so the resultant force and the acceleration get smaller. When the drag equals the weight, the resultant force is zero and the object falls at a constant speed called the terminal velocity.

The same idea works for a car: the top speed is reached when the total resistive force equals the driving force.

Rules to remember

Common mistake

Saying that the object stops or slows down at terminal velocity. The acceleration becomes zero, but the object keeps moving at its greatest, constant speed.

Worked example

A skydiver of mass 80 kg is falling. At one instant the drag force on her is 300 N. What is her acceleration at that instant, and what is the drag force at terminal velocity? (g = 9.81 m s−2)

  1. Weight = mg = 80 × 9.81 = 784.8 N.
  2. Resultant force = weight − drag = 784.8 − 300 = 484.8 N downwards.
  3. Acceleration = resultant force ÷ mass = 484.8 ÷ 80 = 6.06 m s−2.
  4. At terminal velocity the resultant force is zero, so drag = weight = 785 N.

Answer: 6.1 m s−2 downwards; the drag at terminal velocity is about 785 N.

Practice questions

Try each one, then open the answer.

1. A skydiver opens her parachute while falling at terminal velocity. Immediately afterwards

  1. A
    she accelerates downwards
  2. B
    she decelerates because drag now exceeds her weight
  3. C
    she moves upwards
  4. D
    her weight decreases
Show answer

Answer: B. The larger parachute area increases drag above her weight, giving a resultant force upwards; she slows to a new, lower terminal velocity. She never moves upwards.

2. A box is pushed across a rough floor at constant speed by a horizontal force of 30 N. What is the frictional force on the box?

  1. A
    30 N, in the direction opposite to the push
  2. B
    zero, because the box moves at constant speed
  3. C
    less than 30 N, because the box is moving
  4. D
    more than 30 N, otherwise the box would accelerate
Show answer

Answer: A. At constant speed the resultant force is zero, so friction balances the push exactly: 30 N backwards.

3. An object is dropped from rest and falls through air. Which describes its acceleration?

  1. A
    constant and equal to g
  2. B
    starts at zero and increases to g
  3. C
    starts at g and decreases to zero
  4. D
    starts at g and increases
Show answer

Answer: C. At release the speed is zero, so there is no drag and a = g. As speed rises, drag increases, the resultant force falls and the acceleration falls to zero at terminal velocity.

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