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AlgebraFoundation and Higher (some Higher only)

Real-life graphs GCSE questions with answers

8 real-life graphs questions to try, each with the answer and the full working one tap away. Every question here was made and worked out by the Show Working maths engine, not typed in by hand.

Real-life graph questions use distance-time and velocity-time graphs, where the gradient gives the speed or the acceleration. On Higher you also find the distance travelled from the area under a velocity-time graph.

Quiz yourself: 8 questions

Worked example 1: distance-time graphs

Sam cycles from home to a lake and back. The graph shows his journey.
On the way, Sam stops for a rest. For how many minutes does Sam stop the first time?

060120180048121620Time (minutes)Distance from home (km)
  1. A rest shows as a flat part of the graph: the distance from home does not change.
  2. The first flat part goes from 20 minutes to 40 minutes.
  3. 40 − 20 = 20 minutes.

Answer 20 minutes

01 / Quiz yourselfTry it, then tap to check

Real-life graphs questions to try

Work each one out on paper first. Then open the answer and compare your working with ours, step by step.

01 / Distance-time graphsBoth tiers

Sam cycles from home to a friend’s house and back. The graph shows his journey.
Work out Sam’s speed for the first part of the journey, before the first rest. Give your answer in km/h.

06012018004812162024Time (minutes)Distance from home (km)
Show the answer and working
  1. In that part, Sam goes from 0 km to 8 km from home: 8 km.
  2. It takes from 0 to 30 minutes: 30 minutes. There are 60 minutes in an hour, so that is 3060 = 0.5 hours.
  3. Speed = distance ÷ time = 8 ÷ 0.5 = 16 km/h.

Answer 16 km/h

02 / Distance-time graphsBoth tiers

Sam cycles from home to the beach and back. The graph shows his journey.
Work out Sam’s speed on the way home. Give your answer in km/h.

06012018024004812162024Time (minutes)Distance from home (km)
Show the answer and working
  1. In that part, Sam goes from 22 km to 0 km from home: 22 km.
  2. It takes from 130 to 210 minutes: 80 minutes. There are 60 minutes in an hour, so that is 8060 = 43 hours.
  3. Speed = distance ÷ time = 22 ÷ 43 = 16.5 km/h.

Answer 16.5 km/h

03 / Distance-time graphsBoth tiers

Priya cycles from home to the beach and back. The graph shows her journey.
Work out Priya’s speed on the way home. Give your answer in km/h.

0306090120150024681012Time (minutes)Distance from home (km)
Show the answer and working
  1. In that part, Priya goes from 10 km to 0 km from home: 10 km.
  2. It takes from 90 to 130 minutes: 40 minutes. There are 60 minutes in an hour, so that is 4060 = 23 of an hour.
  3. Speed = distance ÷ time = 10 ÷ 23 = 15 km/h.

Answer 15 km/h

04 / Velocity-time graphs: accelerationBoth tiers

A train starts from rest and speeds up, travels at a steady speed, then slows down and stops. The graph shows the velocity during the journey.
Work out the deceleration in the last part of the journey, while slowing down to a stop. Give your answer in m/s².

0481216048Time (seconds)Velocity (m/s)
Show the answer and working
  1. Deceleration is how fast the velocity drops: the steepness (gradient) of the last part of the graph.
  2. The velocity drops from 6 m/s to 0 in 4 seconds (from 8 s to 12 s).
  3. Deceleration = 6 ÷ 4 = 1.5 m/s².

Answer 1.5 m/s²

05 / Velocity-time graphs: accelerationBoth tiers

A car moving at 6 m/s speeds up, travels at a steady speed, then slows down and stops. The graph shows the velocity during the journey.
Work out the acceleration during the first 8 seconds. Give your answer in m/s².

048121620240481216Time (seconds)Velocity (m/s)
Show the answer and working
  1. Acceleration is the gradient of a velocity-time graph.
  2. In the first 8 seconds the velocity goes from 6 m/s to 12 m/s: a change of 6 m/s.
  3. Acceleration = 6 ÷ 8 = 0.75 m/s².

Answer 0.75 m/s²

06 / Velocity-time graphs: accelerationBoth tiers

A bus starts from rest and speeds up, travels at a steady speed, then slows down and stops. The graph shows the velocity during the journey.
Work out the deceleration in the last part of the journey, while slowing down to a stop. Give your answer in m/s².

0481216048Time (seconds)Velocity (m/s)
Show the answer and working
  1. Deceleration is how fast the velocity drops: the steepness (gradient) of the last part of the graph.
  2. The velocity drops from 6 m/s to 0 in 2 seconds (from 12 s to 14 s).
  3. Deceleration = 6 ÷ 2 = 3 m/s².

Answer 3 m/s²

07 / Velocity-time graphs: distanceHigher only

A train starts from rest and speeds up, travels at a steady speed, then slows down and stops. The graph shows the velocity during the journey.
Work out the distance travelled in the first 20 seconds. Give your answer in metres.

0204060800481216Time (seconds)Velocity (m/s)
Show the answer and working
  1. The distance travelled is the area under a velocity-time graph.
  2. Under the first part of the graph is a triangle: 12 × 20 × 12 = 120.
  3. So it travels 120 m.

Answer 120 m

08 / Velocity-time graphs: distanceHigher only

A car starts from rest and speeds up, travels at a steady speed, then slows down and stops. The graph shows the velocity during the journey.
Work out the distance travelled in the first 4 seconds. Give your answer in metres.

048121604812Time (seconds)Velocity (m/s)
Show the answer and working
  1. The distance travelled is the area under a velocity-time graph.
  2. Under the first part of the graph is a triangle: 12 × 4 × 8 = 16.
  3. So it travels 16 m.

Answer 16 m

02 / What's covered3 kinds of question

Real-life graphs at GCSE and where marks go

  • Distance-time graphsBoth tiers
  • Velocity-time graphs: accelerationBoth tiers
  • Velocity-time graphs: distanceHigher only

Worked example 2: velocity-time graphs: distance

A bus starts from rest and speeds up, travels at a steady speed, then slows down and stops. The graph shows the velocity during the journey.
Work out the distance travelled in the first 4 seconds. Give your answer in metres.

0481216048Time (seconds)Velocity (m/s)
  1. The distance travelled is the area under a velocity-time graph.
  2. Under the first part of the graph is a triangle: 12 × 4 × 6 = 12.
  3. So it travels 12 m.

Answer 12 m

A common mistake

Reading a flat section of a distance-time graph as moving at a steady speed. A horizontal line means the distance is not changing, so the person has stopped.

03 / Practise itiPhone and iPad

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