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Broad Topics > Measuring and calculating with units > Speed and acceleration

Dangerous Driver?

Age 16 to 18 Challenge Level:

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

Up and Across

Age 11 to 14 Challenge Level:

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

Speeding Up, Slowing Down

Age 11 to 14 Challenge Level:

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

How Far Does it Move?

Age 11 to 14 Challenge Level:

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.

An Unhappy End

Age 11 to 14 Challenge Level:

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...

John's Train Is on Time

Age 11 to 14 Challenge Level:

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?

Take a Message Soldier

Age 14 to 18 Challenge Level:

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?

Walk and Ride

Age 7 to 14 Challenge Level:

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

Watch the Clock

Age 7 to 11 Challenge Level:

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?

One and Three

Age 14 to 16 Challenge Level:

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. . . .

Triathlon and Fitness

Age 11 to 14 Challenge Level:

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

Nutrition and Cycling

Age 14 to 16 Challenge Level:

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

Age 11 to 14 Challenge Level:

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

Alternative Record Book

Age 14 to 18 Challenge Level:

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

In Order

Age 7 to 11 Challenge Level:

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

Speed-time Problems at the Olympics

Age 14 to 16 Challenge Level:

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

How Do You React?

Age 14 to 16 Challenge Level:

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

Four on the Road

Age 14 to 16 Challenge Level:

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

Speeding Boats

Age 14 to 16 Challenge Level:

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

Graphical Interpretation

Age 14 to 16 Challenge Level:

This set of resources for teachers offers interactive environments to support work on graphical interpretation at Key Stage 4.

Swimmers

Age 14 to 16 Challenge Level:

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

Jumping Gerbils

Age 14 to 16 Challenge Level:

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.

An Average Average Speed

Age 14 to 16 Challenge Level:

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 ?

Motion Sensor

Age 14 to 16 Challenge Level:

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

Take Your Dog for a Walk

Age 7 to 11 Challenge Level:

Use the interactivity to move Mr Pearson and his dog. Can you move him so that the graph shows a curve?

Age 7 to 14

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.

Circuit Training

Age 14 to 16 Challenge Level:

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. . . .

Bus Stop

Age 14 to 16 Challenge Level:

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. . . .

N Is a Number

Age 11 to 14 Challenge Level:

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?

In Constantly Passing

Age 14 to 16 Challenge Level:

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. . . .

Home Time

Age 7 to 11 Challenge Level:

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.

The Hare and the Tortoise

Age 7 to 11 Challenge Level:

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?

Bike Ride

Age 7 to 11 Challenge Level:

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?

Lap Times

Age 14 to 16 Challenge Level:

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

Around and Back

Age 14 to 16 Challenge Level:

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. . . .

Hike and Hitch

Age 14 to 16 Challenge Level:

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. . . .

Illusion

Age 11 to 16 Challenge Level:

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?

Escalator

Age 14 to 16 Challenge Level:

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. . . .

There and Back

Age 14 to 16 Challenge Level:

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?

Speedy Sidney

Age 11 to 14 Challenge Level:

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. . . .