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Speed & Velocity (Oxford AQA IGCSE Physics)

Revision Note

Leander Oates

Expertise

Physics

Velocity

What is the difference between velocity and speed?

  • The velocity of an object is its speed in a given direction

    • Speed is a scalar quantity with a magnitude only

    • Velocity is a vector quantity with a magnitude and direction

Speed vs. Velocity

Two cars travelling at the same speed have different velocities because they travel in different directions. For IGCSE & GCSE Physics revision notes
Two objects can have the same speed but a different velocity

  • The direction of an object's motion can be given as:

    • Compass bearings such as north or south, or 030°

    • Angles to the horizontal or vertical such as 20° to the horizontal

    • A simple direction such as upwards or to the left

    • A positive or negative value such as 20 m / s or −20 m / s

Calculating velocity

  • Velocity can be calculated using:

v space equals fraction numerator space s over denominator t end fraction

  • Where:

    • v = velocity measured in metres per second (m / s)

    • s = displacement measured in metres (m)

    • t = time measured in seconds (s)

  • Velocity, as a vector, has both magnitude and direction

  • The direction of velocity comes from using displacement rather than distance

    • This is because displacement is also a vector quantity, but distance is scalar

Worked Example

A car travels north on a motorway with a velocity of 33 m / s.

Determine the displacement of the car in 2 minutes.

Answer:

Step 1: List the known quantities

  • Velocity, v = 33 m / s

  • Time, t = 2 minutes

Step 2: Convert the values to SI units

  • 1 minute = 60 s

  • Therefore, 2 minutes = 2 × 60 = 120 s

Step 3: Rearrange the velocity equation to make displacement to subject

v space equals fraction numerator space s over denominator t end fraction

  • Multiply both sides by t, then put displacement on the left

s space equals space v space cross times space t

Step 4: Substitute in the known values to calculate

s space equals space 33 space cross times space 120

s space equals space 3960 space straight m space north

Exam Tip

In calculations, the positive value will be assigned to the direction the object is moving in. If multiple objects are travelling in opposite directions, one will be in the positive direction and the other will be in the negative direction. It doesn't matter which direction you assign as positive or negative as long as the opposite direction has the opposite sign.

Average Speed

  • In reality, the speed of an object in motion is often changing

    • Throughout a journey, a car will speed up, slow down, travel at a constant speed and it may also stop at traffic lights

  • Average speed can be calculated for objects in non-uniform motion

average space speed space equals fraction numerator space total space distance space travelled over denominator total space time space taken end fraction

  • This equation for average speed is an adapted form of the velocity equation

v space equals fraction numerator space s over denominator t end fraction

  • Note how, when calculating speed, distance is used instead of displacement

Worked Example

A teacher drives home from work travelling a total distance of 10.6 km. The journey takes 15 minutes.

Calculate the teacher's average speed for the journey.

Answer:

Step 1: List the known quantities

  • Total distance = 10.6 km

  • Total time = 15 minutes

Step 2: Convert the values to SI units

  • 1 km = 1000 m

total space distance space equals space 10.6 space cross times space 1000 space equals space 10 space 600 space straight m

  • 1 minute = 60 s

total space time space equals space 15 space cross times space 60 space equals space 900 space straight s

Step 3: Write out the average speed equation

average space speed space equals fraction numerator space total space distance space travelled over denominator total space time space taken end fraction

Step 4: Substitute the known values to calculate

average space speed space equals fraction numerator space 10 space 600 over denominator 900 end fraction space

average space speed space equals space 12 space straight m divided by straight s

Exam Tip

It is best practice to convert units before you input the value into your calculation. You are less likely to forget and less likely to make mistakes this way.

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    Leander Oates

    Author: Leander Oates

    Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.