Speed and acceleration

  • Around and Back
    problem

    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 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.
  • Lap Times
    problem

    Lap Times

    Age
    14 to 16
    Challenge level
    Can you find the lap times of the two cyclists travelling at constant speeds?
  • Bus Stop
    problem

    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 and in the ratio 5 to 4. The buses travel to and fro between the towns. What milestones are at Shipton and Veston?
  • Bike Ride
    problem

    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?
  • In Order
    problem

    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.

  • Home Time
    problem

    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
    problem

    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?

  • Walk and Ride
    problem

    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?

  • Thunder and Lightning
    problem

    Thunder and Lightning

    Age
    11 to 14
    Challenge level

    How far away was the lightning if the flash and the thunderclap were 6 seconds apart?

  • Don't Be Late
    problem

    Don't Be Late

    Age
    11 to 14
    Challenge level

    Mary is driving to Birmingham Airport. Using her average speed for the entire journey, find how long her journey took.

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