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Subjects · Leaving Cert Applied Maths

Leaving Cert Applied Maths: Resisted motion & drag

How often Resisted motion & drag comes up on the Applied Maths papers, every year it was asked, and questions to try.

HL Asked on 3 of the last 3 Higher Level papers, most recently in 2025. banker

Resisted motion & drag, Higher Level(8 marks)

Quick ones on Resisted motion & drag.

(a)Air resistance on a moving body always acts in which direction?
  1. Vertically downwards
  2. Opposite to its velocity
  3. Vertically upwards
(b)Mass m falls from rest with air resistance kv. Equation of motion (down positive)?
  1. m dv/dt = kv − mg
  2. m dv/dt = mg + kv
  3. m dv/dt = mg − kv
(c)Terminal velocity of mass m falling with air resistance kv²?
  1. √(mg/k)
  2. √(k/mg)
  3. mg/k
Show the answers

(a) Opposite to its velocity

(b) m dv/dt = mg − kv

(c) √(mg/k)

Your turn: Higher Level questions on Resisted motion & drag.

Higher Level

Asked on 3 of the last 3 Higher Level papers, most recently in 2025. banker

Every paper, year by year

YearWhere it came up
2025Q2
2024Q4
2023Q4

Links open the State Examinations Commission’s paper for that year.

More Resisted motion & drag questions

Resisted motion & drag, 3 marks

A particle moves horizontally against resistance kv only. With m v dv/ds = −kv and v = u at s = 0, find v.

  1. v = u e^(−ks/m)
  2. v = u − kt/m
  3. v = u − ks/m
Show the answer

v = u − ks/m

Cancel v: m dv/ds = −k, so v falls linearly with distance: v = u − ks/m. It stops after s = mu/k. The exponential form comes from kv² in v dv/ds, or kv in dv/dt.

Resisted motion & drag, 3 marks

A ball is thrown up and falls back, with air resistance. How do the times up and down compare?

  1. The time up is longer than the time down
  2. The time up is shorter than the time down
  3. They are equal
Show the answer

The time up is shorter than the time down

Going up, drag and gravity both slow the ball, so it stops quickly. Coming down, drag opposes gravity, so it falls the same height more slowly. Without drag the times would be equal.

Resisted motion & drag, 2 marks

A ball is thrown up with air resistance and caught at the same height. Its speed then, compared with its launch speed?

  1. Less than the launch speed
  2. Equal to the launch speed
  3. Greater than the launch speed
Show the answer

Less than the launch speed

Drag does negative work on the way up and on the way down, so the ball loses mechanical energy. It comes back at the same height with less KE, so a lower speed.

Other Applied Maths topics

All of Leaving Cert Applied Maths