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There are **40** NRICH Mathematical resources connected to **Speed and acceleration**, you may find related items under Measuring and calculating with units.

Problem
Primary curriculum
Secondary curriculum
### Triathlon and Fitness

The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Nutrition and Cycling

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Place Your Orders

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Speed-time Problems at the Olympics

Have you ever wondered what it would be like to race against Usain Bolt?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Speeding Boats

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Dangerous Driver?

Was it possible that this dangerous driving penalty was issued in error?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Up and Across

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Speeding Up, Slowing Down

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Far Does it Move?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Take Your Dog for a Walk

Use the interactivity to move Pat. Can you reproduce the graphs and tell their story?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### An Unhappy End

Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### John's Train Is on Time

A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Take a Message Soldier

A messenger runs from the rear to the head of a marching column and back. When he gets back, the rear is where the head was when he set off. What is the ratio of his speed to that of the column?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Watch the Clock

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### One and Three

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400 metres from B. How long is the lake?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Alternative Record Book

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### In Order

Can you rank these quantities in order? You may need to find out extra information or perform some experiments to justify your rankings.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Do You React?

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Four on the Road

Four vehicles travel along a road one afternoon. Can you make sense of the graphs showing their motion?

Age 14 to 16

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Problem
Primary curriculum
Secondary curriculum
### Swimmers

Swimmers in opposite directions cross at 20m and at 30m from each end of a swimming pool. How long is the pool ?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Jumping Gerbils

A conveyor belt, with tins placed at regular intervals, is moving at a steady rate towards a labelling machine. A gerbil starts from the beginning of the belt and jumps from tin to tin.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### An Average Average Speed

My average speed for a journey was 50 mph, my return average speed of 70 mph. Why wasn't my average speed for the round trip 60mph ?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Motion Sensor

Looking at the graph - when was the person moving fastest? Slowest?

Age 14 to 16

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Paradoxes

A paradox is a statement that seems to be both untrue and true at the same time. This article looks at a few examples and challenges you to investigate them for yourself.

Age 7 to 14

Problem
Primary curriculum
Secondary curriculum
### Circuit Training

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever meet at the start again? If so, after how many circuits?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bus Stop

Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant and in the ratio 5 to 4. The buses travel to and fro between the towns. What milestones are at Shipton and Veston?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### N Is a Number

N people visit their friends staying N kilometres along the coast. Some walk along the cliff path at N km an hour, the rest go by car. How long is the road?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### In Constantly Passing

A car is travelling along a dual carriageway at constant speed. Every 3 minutes a bus passes going in the opposite direction, while every 6 minutes a bus passes the car travelling in the same direction. Buses leave the depot at regular intervals; they travel along the dual carriageway and back to the depot at a constant speed. At what interval do the buses leave the depot?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Home Time

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Hare and the Tortoise

In this version of the story of the hare and the tortoise, the race is 10 kilometres long. Can you work out how long the hare sleeps for using the information given?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bike Ride

Nirmala and Riki live 9 kilometres away from the nearest market. They both want to arrive at the market at exactly noon. What time should each of them start riding their bikes?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Walk and Ride

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Lap Times

Can you find the lap times of the two cyclists travelling at constant speeds?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Around and Back

A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns around and heads back to the starting point where he meets the runner who is just finishing his first circuit. Find the ratio of their speeds.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Hike and Hitch

Fifteen students had to travel 60 miles. They could use a car, which could only carry 5 students. As the car left with the first 5 (at 40 miles per hour), the remaining 10 commenced hiking along the road (at 4 miles per hour)...

Age 14 to 16

Challenge Level

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Primary curriculum
Secondary curriculum
### Illusion

A security camera, taking pictures each half a second, films a cyclist going by. In the film, the cyclist appears to go forward while the wheels appear to go backwards. Why?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Escalator

At Holborn underground station there is a very long escalator. Two people are in a hurry and so climb the escalator as it is moving upwards, thus adding their speed to that of the moving steps. ... How many steps are there on the escalator?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### There and Back

Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Speedy Sidney

Two trains set off at the same time from each end of a single straight railway line. A very fast bee starts off in front of the first train and flies continuously back and forth between the two trains. How far does Sidney fly before he is squashed between the two trains?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### On the Road

Four vehicles travelled on a road. What can you deduce from the times that they met?

Age 14 to 16

Challenge Level