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Subjects · Leaving Cert Applied Maths

Leaving Cert Applied Maths: Displacement & velocity graphs

How often Displacement & velocity graphs comes up on the Applied Maths papers, every year it was asked, and questions to try.

HL Asked on 1 of the last 3 Higher Level papers, most recently in 2025.

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

Displacement & velocity graphs, Higher Level(7 marks)

Quick ones on Displacement & velocity graphs.

(a)On a velocity–time graph, what does the area under the graph give?
  1. Acceleration
  2. Displacement
  3. Average speed
(b)What does the gradient of a velocity–time graph give?
  1. Average speed
  2. Displacement
  3. Acceleration
(c)v–t graph: 0 to 12 m/s in 4 s, steady for 8 s, then back to 0 in 6 s. Total distance?
  1. 156 m
  2. 108 m
  3. 216 m
Show the answers

(a) Displacement

(b) Acceleration

(c) 156 m

Your turn: Higher Level questions on Displacement & velocity graphs.

Higher Level

Asked on 1 of the last 3 Higher Level papers, most recently in 2025.

Every paper, year by year

YearWhere it came up
2025Q9
2024Not asked
2023Not asked

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

More Displacement & velocity graphs questions

Displacement & velocity graphs, 3 marks

What does part of a velocity–time graph lying below the time axis show?

  1. Deceleration of the body
  2. The body is at rest for that time
  3. Motion in the negative direction
Show the answer

Motion in the negative direction

A negative velocity means the body moves the opposite way. Deceleration is a falling speed, which is about the slope, not the sign. Area below the axis counts as negative displacement.

Displacement & velocity graphs, 2 marks

A displacement–time graph curves and gets steeper and steeper. What does that show?

  1. The body is slowing down
  2. The speed is increasing
  3. The speed is constant
Show the answer

The speed is increasing

The gradient of an s–t graph is the velocity. A steeper and steeper curve means the velocity is growing, so the body is accelerating.

Ordinary Level

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

Every paper, year by year

YearWhere it came up
2025Q10
2024Q1
2023Q6

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

More Displacement & velocity graphs questions

Displacement & velocity graphs, 2 marks

What does the slope of a velocity–time graph give?

  1. Displacement
  2. Distance from the start
  3. Acceleration
Show the answer

Acceleration

Slope = change in velocity ÷ change in time, which is acceleration in m s⁻². A steeper line means a bigger acceleration.

Displacement & velocity graphs, 3 marks

A v–t graph is a straight line from (0 s, 0) to (10 s, 30 m s⁻¹). Distance travelled?

  1. 3 m
  2. 150 m
  3. 300 m
Show the answer

150 m

The area is a triangle: ½ × base × height = ½ × 10 × 30 = 150 m. 300 m forgets the ½; 3 is the slope (acceleration).

Displacement & velocity graphs, 2 marks

What does the area under a velocity–time graph give?

  1. Displacement
  2. Acceleration
  3. Time taken
Show the answer

Displacement

Area = velocity × time, which is distance moved in metres. Split the region into rectangles, triangles or trapeziums to find it.

Other Applied Maths topics

All of Leaving Cert Applied Maths