Graphs in practical situations

The speed-time graph represents the opening 60 seconds of a train journey. The vertical axis is marked Speed (m/s) up to 15, while the horizontal axis is marked Time (s) up to 60. A straight line is drawn from $(0, 0)$ to $(60, 15)$.

Feb/March 2017

Each day, Anand, Rahul, and Samir travel from school to the park.

Feb/March 2018

Find the temperature at 01 00 from the information given.

Feb/March 2019

Determine the temperature at 01 00.

Feb/March 2019

The speed-time graph represents the journey during the initial 50 seconds.

Feb/March 2019

Mr Patel is making a train trip into the city, with the library as his destination. The travel graph traces his journey from Keela station to the library. The graph has: Vertical axis: Distance (km), marked up to 36. Horizontal axis: Time from 09 00 to 12 00. Stations marked on the distance axis: Keela station at 0 km, Lanay station at 12 km, City station at 28 km, Library at 32 km. A line traces the journey from Keela station at 09 00 to the library at 10 00.

Feb/March 2019

Write down the fare for a 4 km trip.

Feb/March 2020

The speed-time graph for part of a car journey is shown in the diagram.

Feb/March 2023

The speed-time graph provides data for a bus journey. The vertical axis is Speed (m/s) and the horizontal axis is Time (seconds). Speed rises linearly from 0 to 15 m/s during the first 20 seconds, remains constant at 15 m/s until 140 seconds, then falls linearly to 0 by 190 seconds. The graph is labelled NOT TO SCALE.

Feb/March 2024

A tram departs from a station, speeds up for 2 minutes until its speed is 12 metres per second, then travels at that speed for 1 minute. After that, it slows down for 3 minutes and comes to rest at the next station. The diagram gives the speed-time graph for this trip. Speed (metres per second) is shown on the vertical axis, while Time (minutes) is shown on the horizontal axis.

May/June 2015

The diagram presents the speed-time graph for 120 seconds of a car journey.

May/June 2015

A speed-time graph (not to scale) depicts a car beginning from rest, increasing its speed for $u$ seconds until it reaches $10\,\text{m s}^{-1}$, and then continuing at $10\,\text{m s}^{-1}$ for $2u$ seconds. The distance covered in the first $3u$ seconds is 125 m.

May/June 2015

On the grid, the train’s travel graph is shown for a journey from Audley to Cawley, with a stop at Brookland.

May/June 2015

The travel graph depicts the train’s trip from $A$ to $C$, with a stop at $B$.

May/June 2015

Biscuits and cakes constraints.

May/June 2015

Here is a graph used to convert dollars ($) into pounds (£). The vertical axis is marked Pounds (£). The horizontal axis is marked Dollars ($). The line is straight and runs through the origin.

May/June 2016

Sonali travels by bicycle from home to the sports centre. The travel graph traces her trip. The vertical axis gives distance in km and includes the labels Home and Sports centre. The horizontal axis gives time from 15:30 to 17:45.

May/June 2016

Alice departs from home at $08\,15$ and moves at $80$ metres per minute, reaching her friend’s house half an hour afterwards.

May/June 2016

The diagram presents a speed-time graph for a car's journey. Speed is shown in m/s and time is measured in seconds. It rises from 0 to 12.5 m/s in 20 s, remains constant until 220 s, and then drops to 0 by 280 s. The diagram is not drawn to scale.

May/June 2017

The diagram presents the travel graph of a bus moving between three towns. The vertical axis is marked Distance (km), with Seaton at 0 km, Tyneland at 16 km and Wegmouth at 32 km. The horizontal axis is marked Time, running from 11 00 to 13 00.

May/June 2017

The train’s journey is represented by the distance-time graph.

May/June 2017

The speed-time graph gives details of a tram journey between two stations. Speed is shown in m/s and time is shown in seconds. The diagram is NOT TO SCALE.

May/June 2018

State the temperature at midnight.

May/June 2018

A speed-time graph, drawn not to scale, plots speed (km/h) against time (seconds) for the first 60 seconds of a car journey. From 0 to 40 seconds the car moves at $90\text{ km/h}$, and from then until 60 seconds it slows uniformly to $0$.

May/June 2018

Louise sets off from home at 09 55 and rides the 5.6 km to the supermarket at a steady pace. She needs 15 minutes to make the trip.

May/June 2018

Write down the day that had the coldest temperature.

May/June 2018

Michael’s route from his home to the beach is represented by the travel graph. The vertical axis gives Distance (km), marked from Home (0) up to Beach (12). The horizontal axis shows Time running from 08:00 to 11:00. A straight line climbs from 08:00 to around 09:15 and reaches 8 km, followed by a flat section up to 10:00, and then another straight line rises to 12 km at 11:00.

May/June 2019

Calculate the difference between these two temperatures.

May/June 2019

The diagram gives data for the final 70 seconds of a car journey. The vertical axis is labelled Speed (m/s) and runs up to 20, while the horizontal axis is labelled Time (seconds) and extends from 0 to 70. The speed remains steady at 20 m/s from 0 to 60 seconds, then falls linearly to 0 m/s at 70 seconds. The diagram is labelled NOT TO SCALE.

May/June 2019

The travel graph presents one section of a train trip from station $A$ to station $C$. The vertical axis is labelled Distance (km), with Station A at 0 km, Station B at 80 km and Station C at 150 km. The horizontal axis is labelled Time, ranging from 12:30 to 15:30.

May/June 2019

The travel graph below plots distance (km) against time from 12:00 to 16:00.

May/June 2021

A car is initially at rest, then it accelerates at a rate of $3\text{ m s}^{-2}$ for 4 seconds. It then continues at a constant speed for 10 seconds. The diagram presents the speed-time graph for this trip.

May/June 2021

The diagram presents the speed-time graph covering the first 180 seconds of a train journey. The vertical axis carries the label Speed (m/s), while the horizontal axis is labelled Time (s). The graph rises steadily from 0 m/s at 0 s to 9 m/s at 50 s, then stays at 9 m/s until 180 s.

May/June 2021

A speed-time graph is given for a car journey lasting 24 seconds. The vertical axis is marked Speed (m/s) up to 12, while the horizontal axis is marked Time (s) from 0 to 24. The speed remains constant from 0 to 16 seconds, then drops in a straight line to 0 at 24 seconds. NOT TO SCALE.

May/June 2022

Annette rides her bicycle for a distance of $70\text{ km}$ from Midville to Newtown. After leaving Midville, she travels for $1$ hour $30$ minutes at a steady speed of $20\text{ km/h}$, then pauses for $30$ minutes. She then completes the trip to Newtown at a steady speed of $16\text{ km/h}$. A distance-time grid is given, with the vertical axis marked Distance (km) from $0$ to $80$ and the horizontal axis marked Time (h) from $0$ to $5$.

May/June 2022

Abdul sketches this speed-time graph for a journey. It is split into four parts, A, B, C and D. The vertical axis is labelled Speed (m/s). The horizontal axis is labelled Time (s).

May/June 2022

The distance-time graph presents details of Kai’s trip from home to the office. The vertical axis is labelled Distance (km), and the horizontal axis is labelled Time. Home is shown at 0 km, while Office is shown at the top.

May/June 2023

Diego and Javier are two friends who meet at a swimming pool. The travel graph records Diego’s bicycle trip from his home to the swimming pool.

May/June 2023

540 South African rands is equal to 50 Australian dollars.

May/June 2023

State the time at which the boat departs from A.

May/June 2023

The travel graph illustrates a bus trip. The vertical axis is labelled Distance (km), while the horizontal axis is labelled Time and runs from 14 00 to 16 00. The distance rises from 0 km at 14 00 to 12 km at 15 00, stays at 12 km until around 15 30, and then falls to 0 km again at 16 00.

May/June 2024

A speed–time graph is used to give details of a car journey. Speed is in m/s and time is in seconds. The car increases speed from 0 to 16 m/s in 30 s, then continues at a steady speed up to 240 s, before slowing down to 0 by 320 s.

May/June 2024

Ky rides from his office to a meeting and then travels back again. The travel graph illustrates the time he spends at the meeting and his return journey. Time is shown from 09:00 to 12:00 along the horizontal axis, while distance from the office (km) goes from 0 to 15 on the vertical axis. A flat section at 14 km represents the time at the meeting, followed by a straight downward-sloping line to show the journey back to the office.

May/June 2025

Tim makes the journey home from work. The travel graph represents his trip. The vertical axis is labelled "Distance from home (km)" with 0 at Home and 36 at Work. The horizontal axis is labelled "Time" from 14 00 to 15 30.

May/June 2025

How many minutes does Maria take to travel from home to the shopping mall?

Oct/Nov 2015

A car goes past a checkpoint at $t = 0$ seconds, moving at $8\text{ m/s}$. It keeps this speed for 10 seconds. It then slows down at a constant rate and comes to rest when $t = 55$ seconds.

Oct/Nov 2015

The diagram depicts a car’s speed-time graph. The car moves at 45 km/h for 20 seconds. It then slows down over 10 seconds until it comes to rest. On the graph, speed (km/h) is shown on the vertical axis and time (seconds) on the horizontal axis, with 0, 10, 20, and 30 seconds marked. The diagram is marked NOT TO SCALE.

Oct/Nov 2015

The grid presents the train’s travel graph as it goes from Dexford to Fintown, with a stop at Emley.

Oct/Nov 2015

Ali is buying $x$ rose bushes and $y$ lavender bushes. He buys: no fewer than 5 rose bushes; no more than 8 lavender bushes; no more than 15 bushes altogether; and a greater number of lavender bushes than rose bushes.

Oct/Nov 2015

The distance-time graph represents the cyclist’s first 10 minutes of travel. Its vertical axis is labelled "Distance (km)" and runs from 0 to 4, while its horizontal axis is labelled "Time (minutes)" and runs from 0 to 10. The graph contains a straight line rising from (0,0) to (6,2), then a horizontal segment from 6 to 7 minutes at a distance of 2 km, and finally another straight line rising from 7 minutes at 2 km to 10 minutes at 3.5 km.

Oct/Nov 2016

The diagram gives the distance-time graph covering the first 65 minutes of a bicycle trip.

Oct/Nov 2016

The diagram presents the distance-time graph covering the first 65 minutes of a bicycle ride. Distance (km) is plotted on the vertical axis, while Time (minutes) is shown on the horizontal axis. The ride is split into four labelled sections A, B, C and D.

Oct/Nov 2016

This graph illustrates Gianna’s trip to work.

Oct/Nov 2016

Alvin exchanges some dollars ($) for euros (€). When he exchanges $\$100$, he is given €60.

Oct/Nov 2017

Petra sets off in her car and starts from rest. She speeds up at a constant rate of $0.4\ \text{m s}^{-2}$ for 30 seconds. After that, she continues moving at a steady speed for 40 seconds.

Oct/Nov 2017

Work out what the temperature was at midnight.

Oct/Nov 2017

The figure presents a speed-time graph.

Oct/Nov 2017

State the temperature indicated by the arrow.

Oct/Nov 2017

The graph summarises the train's trip between two stations. The vertical axis is labelled 'Speed (km/h)'. The horizontal axis is labelled 'Time of day'. Speed rises steadily from 0 at 09 00 to 126 km/h at 09 04, stays at 126 km/h until 09 48, and then falls steadily to 0 at 09 55. The diagram is marked as not to scale.

Oct/Nov 2017

Shohan rides his cycle from home to the library, stopping at the post office along the way. His trip is shown on the distance-time graph. The vertical axis is marked "Distance from home (km)" and the horizontal axis is marked "Time" from $10\,00$ to $12\,00$. Home is at $0$ km and Library is at $10$ km.

Oct/Nov 2018

The diagram presents a conversion graph linking pounds (£) and dollars ($).

Oct/Nov 2018

Find the temperature at midnight.

Oct/Nov 2018

The diagram presents the speed-time graph for the first $T$ seconds of a car journey. The vertical axis is marked Speed $(\text{m/s})$ and runs from $0$ to $12$, while the horizontal axis is labelled Time (seconds). The graph is a straight line from $(0,0)$ to $(10,12)$, followed by a horizontal segment at speed $12$ up to time $T$. The diagram is not drawn to scale.

Oct/Nov 2018

The diagram presents the speed-time graph for one section of a journey made by two people, a runner and a walker.

Oct/Nov 2018

Juan goes from his home to a shop. The travel graph represents his journey. The vertical axis is Distance (km). The horizontal axis is Time. Home is at 0 km and the shop is at 14 km. The graph shows travel starting from 13:00 onwards.

Oct/Nov 2019

Sara travels from home to school on foot. Her journey is represented on the distance–time graph. On the vertical axis, Distance (km) is labelled from 0 to 3. On the horizontal axis, Time runs from 08:00 to 09:00. The graph has a line sloping upwards from home at 08:00 to about 1.2 km at 08:10, then a flat section until about 08:25, then another upward line to about 2.4 km at about 08:45, and finally a horizontal line to 09:00 at school.

Oct/Nov 2019

The diagram displays a conversion graph between dollars and Kenyan shillings.

Oct/Nov 2019

A speed-time graph is shown, and it is not drawn to scale. A car travels at 20 m/s for 15 seconds before it comes to rest by slowing down at $2.5\,\text{m s}^{-2}$.

Oct/Nov 2019

The diagram illustrates the speed-time graph for 70 seconds of a car journey. Speed is measured in m/s and time is measured in seconds.

Oct/Nov 2019

Hua rides her bicycle from home to the library. The journey is shown on the travel graph. The vertical axis is labelled Distance from home (km), and the horizontal axis is labelled Time. Home is at $0$ km, while Library is at $12$ km.

Oct/Nov 2020

The diagram presents the speed-time graph for the first 100 seconds of a journey made by a car and a motorbike. Diagram text: The vertical axis is labelled "Speed (m/s)" and extends to 20. The horizontal axis is labelled "Time (s)" and extends to 100. A solid line marked "Car" remains at 18 m/s from 0 to 60 s, then drops in a straight line to 6 m/s at 100 s. A dashed horizontal line labelled "Motorbike" is drawn at 12 m/s.

Oct/Nov 2020

The diagram presents the speed-time graph for the first 40 seconds of a cycle ride. Speed is measured in m/s and time is measured in seconds.

Oct/Nov 2020

This diagram is a speed-time graph covering the last 40 seconds of a car journey. The vertical axis is labelled Speed (m/s), and the horizontal axis is labelled Time (seconds). At $t=0$, the speed is $v$. From 0 to 24 seconds, the speed rises in a straight line to $v+10$. From 24 to 40 seconds, the speed falls in a straight line to 0. The diagram is marked NOT TO SCALE.

Oct/Nov 2020

A car begins from rest and accelerates uniformly at $0.7\,\text{m s}^{-2}$ for 20 seconds, so that it then attains a steady speed of $14\,\text{m s}^{-1}$. After that, it continues at $14\,\text{m s}^{-1}$ over a distance of $210\,\text{m}$. Next, the car slows down at a constant rate of $1.4\,\text{m s}^{-2}$ until it stops. A speed-time grid is shown.

Oct/Nov 2021

Explain what is taking place between 1409 and 1410.

Oct/Nov 2021

This diagram presents the speed-time graph for the first 15 seconds of a car journey. The speed rises at a constant rate from 0 to $14\text{ m/s}$ in the opening 5 seconds, and then it stays unchanged until 15 seconds.

Oct/Nov 2022

The diagram presents the speed-time graph for a car during part of its journey. Speed (m/s) increases steadily from 0 to 30 in 15 seconds, and then stays at 30 m/s. The time axis is in seconds. Diagram marked NOT TO SCALE. The car begins at rest and speeds up at a constant rate for 15 seconds before settling at a steady speed of 30 m/s.

Oct/Nov 2022

Sandy Cove lies on the route from Bay Park to Ocean Park.

Oct/Nov 2022

The diagram presents the speed-time graph for part of a journey involving two vehicles, a car and a bus. The bus moves with constant speed $v$. The car accelerates uniformly from 10 m/s at $t=0$ to 24 m/s at $t=18$ seconds, and then continues at constant speed up to $t=40$ seconds. The diagram is labelled NOT TO SCALE.

Oct/Nov 2022

The diagram gives a speed-time graph for 16 seconds of a car journey. The vertical axis is Speed (m/s), while the horizontal axis is Time (seconds). From 0 to 12 seconds the speed stays constant at 10 m/s. From 12 to 16 seconds the speed drops linearly to 0. The diagram is marked NOT TO SCALE.

Oct/Nov 2023

The diagram gives the speed-time graph for the first 17 seconds of a car journey. NOT TO SCALE. The speed rises in a straight line from $0\,\text{m s}^{-1}$ at $0$ seconds to $20\,\text{m s}^{-1}$ at $10$ seconds, then stays at $20\,\text{m s}^{-1}$ until $17$ seconds.

Oct/Nov 2024

Samir sets off from home at 2 pm. He runs 6 km to a café at a steady speed of 8 km per hour. He then pauses to rest for 1 hour. After that, he walks back home at a steady speed and gets home at 4.36 pm.

Oct/Nov 2024

Bob goes from town A to town B. The travel graph represents his trip.

Oct/Nov 2025

The diagram gives the speed-time graph for part of a car journey. Speed rises linearly from 60 km/h at 0 minutes to 80 km/h at 15 minutes, then falls linearly to 0 km/h at 25 minutes.

Oct/Nov 2025