Graphs in practical situations

Kim and Lee are running a 2000 metre cross-country route that begins at $P$ and finishes at $Q$. Lee sets off 1 minute after Kim. Their distance-time graphs are shown in the diagram.

May/June 2015

The diagram shows a train’s trip between two stations on a speed-time graph.

May/June 2015

The diagram presents the speed-time graph of a train that slows from $20\text{ m/s}$ to rest in $T$ seconds.

May/June 2016

The diagram shows the speed-time graph for one section of a car journey. The car’s retardation from $t=8$ to $t=12$ is $4\text{ m s}^{-2}$.

May/June 2016

It is stated that $100$ dollars $(\$)$ is the same as $56$ pounds $(\pounds)$.

May/June 2016

This distance-time graph represents a red bus’s trip from a village to a town.

May/June 2017

The speed-time graph shown represents 25 seconds of a car journey. Starting at a speed of $v\,\text{m s}^{-1}$, the car decreases uniformly to $12\,\text{m s}^{-1}$ in 15 seconds. It then keeps a constant speed for another 10 seconds.

May/June 2017

The graph of speed against time shows how a car moves.

May/June 2018

The inequalities $2\le x\le 8$, $5\le y\le 10$, $x+y\ge10$ define region $R$. On the diagram, shade and label region $R$.

May/June 2018

This diagram shows the speed-time graph for $60$ seconds of a train’s trip. At the start of this section, the train is moving at $u\ \text{m s}^{-1}$.

May/June 2018

A car sets off from rest. For the first $20$ seconds, it accelerates uniformly until its speed becomes $15\,\text{m s}^{-1}$. After that, it continues at a steady speed of $15\,\text{m s}^{-1}$ for $40$ seconds.

May/June 2019

Lara takes a cycle ride, and her journey is represented on the distance-time graph.

May/June 2021

The graph gives the cost, in dollars, of buying a length of fabric $t$ metres long.

May/June 2022

The diagram presents the cyclist’s journey as a speed-time graph.

May/June 2022

The diagram presents the speed-time graph for a section of a car’s journey.

May/June 2023

The distance-time graph represents Maya’s trip from the office to the factory. The diagram gives the cyclist’s distance-time graph. The cyclist covers $d$ metres from home to a lake and then heads back home.

May/June 2023

The diagram gives the cyclist’s distance-time graph for the opening two stages of a race, $AB$ and $BC$.

May/June 2024

The diagram displays the cyclist’s journey on a speed-time graph.

May/June 2025

The diagram gives the speed-time graph for a section of a car’s journey.

May/June 2025

For a moving object, its distance, $d$ metres, from an observer after $t$ minutes is given by $d = t^2 + \frac{48}{t} - 20$.

Oct/Nov 2015

The speed-time graph shown represents part of a car's journey.

Oct/Nov 2016

The diagram depicts the speed-time graph of a car that reduces its speed from $30\text{ m s}^{-1}$ to $12\text{ m s}^{-1}$ over $20$ seconds, and then continues at $12\text{ m s}^{-1}$.

Oct/Nov 2016

A train runs between two stations and is at rest both when it sets off and when it arrives. For the first $30$ seconds, it speeds up uniformly from rest until its speed is $20\text{ m s}^{-1}$; during the following $60$ seconds it continues at a steady $20\text{ m s}^{-1}$; over the final $20$ seconds it decelerates uniformly until it comes to rest.

Oct/Nov 2018

This diagram shows the train’s journey on a speed-time graph for part of the trip.

Oct/Nov 2019

The diagram shows the train’s motion on a speed-time graph for part of its journey.

Oct/Nov 2019

This diagram shows Safira’s distance-time graph for her trip from home to a shop and then back home again. She sets off at $08\,15$ and gets back at $08\,50$.

Oct/Nov 2020

The diagram presents the cyclist’s speed-time graph for the opening part of the journey.

Oct/Nov 2021

The diagram illustrates Sam’s speed-time graph for the trip from home to work.

Oct/Nov 2022

The diagram presents the speed-time graph for one section of a car journey.

Oct/Nov 2023

The speed-time graph in the diagram represents part of the journey for cyclists $A$ and $B$.

Oct/Nov 2023

The diagram presents a speed-time graph for the journey.

Oct/Nov 2024