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AS · Practice questions · Motion with resistance

Until the forces balance.

Six original Cambridge-style questions on the forces at each stage of a fall, on finding terminal velocity, on velocity-time graphs, and on the skydiver and crumpled-paper cases.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
Keep these straight

Drag grows, then balances.

01
Analysis
[3 marks]

An object is released from rest and falls through air. Describe the forces on it and its acceleration at three stages: immediately after release, partway down while speeding up, and at terminal velocity.

  • At release: drag is zero, so the only force is weight and the acceleration is g (maximum). ✓
  • Speeding up: drag has grown but is still less than weight, so the resultant is downward and the acceleration is positive but decreasing. ✓
  • Terminal velocity: drag equals weight, the resultant is zero, so the acceleration is zero and the speed is constant. ✓
02
Analysis
[2 marks]

A raindrop of weight 4.0 × 10⁻⁵ N falls at terminal velocity. State the drag force acting on it, and the resultant force.

  • At terminal velocity drag = weight = 4.0 × 10⁻⁵ N, acting upward. ✓
  • The resultant force is zero. ✓
03
Analysis
[3 marks]

A ball of mass 0.20 kg falls through a liquid in which the drag force is D = 0.40v (D in N, v in m s⁻¹). Taking g = 9.8 m s⁻², find its terminal velocity.

  • Weight = mg = 0.20 × 9.8 = 1.96 N. ✓
  • At terminal velocity drag = weight: 0.40v = 1.96. ✓
  • v = 1.96 / 0.40 = 4.9 m s⁻¹. ✓
04
Analysis
[2 marks]

Sketch in words the velocity-time graph for a stone dropped from rest into deep water where there is significant drag, until it reaches terminal velocity.

  • The curve starts steep (gradient g) at the origin. ✓
  • The gradient decreases as drag builds, and the curve flattens to a horizontal line at the terminal velocity. ✓
05
Analysis
[3 marks]

A skydiver is falling at a steady terminal velocity and then opens a parachute. Explain, in terms of forces, why the diver slows down and then falls at a new steady speed.

  • The parachute increases the area, so the drag suddenly becomes much larger than the weight. ✓
  • The resultant force is now upward, so the diver decelerates. ✓
  • As the speed falls, the drag decreases until it again equals the weight, giving a new, lower terminal velocity. ✓
06
Analysis
[2 marks]

A student claims that at terminal velocity "there is no force on the object". Correct this statement and give the precise condition that holds at terminal velocity.

  • There are still two forces, the weight and the drag; they are equal and opposite. ✓
  • The correct condition is that the resultant force is zero, so the acceleration is zero and the velocity is constant. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.