Where can I download free velocity time graphs PDF worksheets with answers?

On this MathsLinks page you can download free printable velocity time graphs PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, Maths Genie, Corbett Practice, Corbett Textbook, Maths Made Easy, plus a printable one-page velocity time graphs revision guide.

What GCSE grade is velocity time graphs (8G)?

Velocity time graphs (topic code 8G) is a Grade 8+ algebra topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Velocity time graphs Worksheets (PDF) with Answers — GCSE Maths

Free Velocity time graphs PDF Worksheets & Answers

Grade 8+ • Topic 8G

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Maths Made Easy MME worksheet & model answers	Qs	Ans
Dr Frost GCSE worksheet & solutions	Qs	Ans
Naiker Maths Exam question booklet & solutions	Qs	Ans
1st Class Maths (Edxl) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (AQA) AQA exam questions & solutions	Qs	Ans
Metatutor Topic worksheet & worked solutions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
E Classroom GCSE topic booklet & answers	Qs	Ans
PMT (Edxl) Edexcel GCSE topic questions & solutions	Qs	Ans
PMT (AQA) AQA GCSE topic questions & solutions	Qs	Ans
PMT (IGCSE) Edexcel IGCSE topic questions & solutions	Qs	Ans
Cognito Interactive online lesson & practice	Page

Grade 8+ topics
8A - Quad. sim. equations	8B - Transforming graphs y=f(x)
8C - Algebraic proof	8D - Completing the square
8E - Quadratic inequalities	8F - Quadratic sequences
8G - Velocity time graphs	8H - Circles and tangents
8J - Circle theorem proof	8K - Vector proof
8L - Probability equation questions	8M - Invariant points
8N - Spheres, cones and cylinders	8P - Volume of a frustum

Explanation:

On a velocity-time graph, the gradient represents acceleration (change in velocity ÷ time) and the area under the graph represents distance travelled. For straight-line graphs, split the region into triangles and trapeziums; for curved graphs, draw a tangent at the given point to estimate instantaneous acceleration.

To estimate the distance under a curve using strips of equal width, split the area into a triangle and trapeziums: if the curve is concave down, the chords lie below the curve so your answer is an underestimate; if concave up, it is an overestimate.

Example 1: A car accelerates uniformly from rest to 20 m/s in 8 s, travels at 20 m/s for 15 s, then decelerates to rest in 5 s. Find the deceleration and total distance.

Solution:

Deceleration = 205 = 4 m/s² (gradient = −4 m/s²)

Total time = 8 + 15 + 5 = 28 s (top side = 15 s)

Area of trapezium = 15 + 282 × 20 = 430 m

Answer: 4 m/s² and 430 m

Example 2: Velocity v (m/s) at t = 0, 2, 4, 6 s is 0, 5, 14, 27. Estimate the distance travelled in 6 s using 3 strips of equal width.

Solution:

Strip 1 (0 to 2): 12 × 2 × 5 = 5 m

Strip 2 (2 to 4): 5 + 142 × 2 = 19 m

Strip 3 (4 to 6): 14 + 272 × 2 = 41 m

Answer: 5 + 19 + 41 = 65 m

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Velocity time graphs Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 GCSE Jun 2019 2H Q14 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

A car moves from rest.
The graph gives information about the speed, v metres per second, of the car t seconds after it starts to move.

(a) Calculate an estimate of the gradient of the graph at t = 15 [3 marks]

Describe what your answer to part (i) represents. [1 mark]

Worked Solution & Mark Scheme (4 marks)

Part (a) Solution:

(Average speed = distance ÷ time)
Tangent at t = 15 has gradient ≈ 7.5 ÷ 9 = 0.83 M2 A1

Answer (a): 0.83

Part Solution:

(Average speed = distance ÷ time) C1

Answer : The acceleration of the car (or rate of change of speed)

Past Paper Example 2 GCSE Nov 2017 3H Q18 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

Here is a speed-time graph for a train.

(a) Work out an estimate for the distance the train travelled in the first 20 seconds.
Use 4 strips of equal width. [3 marks]

(b) Is your answer to (a) an underestimate or an overestimate of the actual distance the train travelled?
Give a reason for your answer. [1 mark]

Worked Solution & Mark Scheme (4 marks)

Part (a) Solution:

(Average speed = distance ÷ time)
Strip width = 5 s M1
speeds at t = 0, 5, 10, 15, 20 are 0, 2, 5, 10, 18 m/s M1
Area = (0.5 × 5 × 2) + (0.5 × 5 × (2+5)) + (0.5 × 5 × (5+10)) + (0.5 × 5 × (10+18)) = 5 + 17.5 + 37.5 + 70 = 130 m A1

Answer (a): 130 m

Part (b) Solution:

(Average speed = distance ÷ time)
Overestimate since chords lie above the curve C1

Answer (b): Overestimate, because the tops of the trapeziums lie above the curve (the curve is convex)

Past Paper Example 3 GCSE Nov 2021 3H Q21 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

Here is a speed-time graph showing the speed, in metres per second, of an object t seconds after it started to move from rest.

(a) Using 3 trapeziums of equal width, work out an estimate for the area under the graph between t = 1 and t = 4 [3 marks]

(b) What does this area represent? [1 mark]

Worked Solution & Mark Scheme (4 marks)

Part (a) Solution:

(Average speed = distance ÷ time)
Ordinates at t = 1, 2, 3, 4 are 4, 6, 7.2, 7.8. Area = ½(1)(4 + 6) + ½(1)(6 + 7.2) + ½(1)(7.2 + 7.8) = 5 + 6.6 + 7.5 = 19.1 M2 A1

Answer (a): 19.1

Part (b) Solution:

(Average speed = distance ÷ time)
Distance travelled in metres B1

Answer (b): Distance travelled (between t = 1 and t = 4 seconds)

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Velocity time graphs

Free Velocity time graphs PDF Worksheets & Answers

Guide to Velocity time graphs: Explanation, Diagrams & Worked Examples

GCSE Past Paper Velocity time graphs Questions & Answers