Speed & Velocity (CIE IGCSE Physics: Co-ordinated Sciences (Double Award))

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Speed

  • The speed of an object is defined as

 Distance travelled per unit time

  • Speed is a scalar quantity
    • This is because it only contains a magnitude (without a direction)

  • For objects that are moving at a constant speed, the equation for calculating speed is:

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

  • Where:
    • v = speed, measured in metres per second (m/s)
    • s = distance travelled, measured in metres (m)
    • t = time, measured in seconds (s)

Average speed

  • The speed of an object can vary throughout its journey
  • Therefore, it is often more useful to know an object's average speed

Examples of average speeds

Person vs Bee, downloadable IGCSE & GCSE Physics revision notes

A hiker might have an average speed of 2.0 m/s, whereas a particularly excited bumble bee can have average speeds of up to 4.5 m/s

 

  • The equation for calculating the average speed of an object is:

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

  • Average speed considers the total distance travelled and the total time taken

Average Speed Triangle, downloadable IGCSE & GCSE Physics revision notes

Formula triangle for average speed, distance moved and time taken

How to use formula triangles

  • Formula triangles are really useful for knowing how to rearrange physics equations
  • To use them:
  1. Cover up the quantity to be calculated, this is known as the 'subject' of the equation
  2. Look at the position of the other two quantities
    • If they are on the same line, this means they are multiplied
    • If one quantity is above the other, this means they are divided - make sure to keep the order of which is on the top and bottom of the fraction!

  • In the example below, to calculate average speed, cover-up the variable speed so that only distance and time are left
    • The equation is revealed as:

speed space equals fraction numerator space distance over denominator time end fraction

Formula Triangle, downloadable AS & A Level Physics revision notes

To use a formula triangle, simply cover up the quantity you wish calculate and the structure of the equation is revealed

Worked example

Planes fly at typical average speeds of around 250 m/s.

Calculate the distance travelled by a plane moving at this average speed for 2 hours.

Answer:

Step 1: List the known quantities

    • Average speed = 250 m/s
    • Time taken = 2 hours

Step 2: Write the relevant equation

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

Step 3: Rearrange to make distance moved the subject

distance space travelled space equals space average space speed space cross times space time space taken

Step 4: Convert any units

  • The time given in the question is not in standard units
  • Convert 2 hours into seconds:

2 space hours space equals space 2 space cross times space 60 space cross times space 60 space

2 space hours space equals space 7200 space straight s

Step 5: Substitute the values for average speed and time taken

distance space travelled space equals space 250 space cross times space 7200

distance space travelled space equals space 1 space 800 space 000 space straight m

Examiner Tip

Rearranging equations is an important skill in Physics. You can use the equation triangles to help you practice, but it is better not to rely on them because they do not work for all equations you may need to rearrange in the exam.

Velocity

Extended tier only

  • Velocity is a vector quantity with magnitude and direction

  • Velocity is defined as:

Speed in a given direction

  • The direction of a velocity can be given in words
    • For example, 20 m/s east
  • Or the direction of velocity can be given using a positive or negative value
    • For example, −20 m/s
  • A positive direction is typically in the direction of the initial motion, to the right, or upward
  • A negative velocity is typically in the opposite direction to the initial velocity, to the left, or downward

Comparing speed and velocity

Speed & Velocity, downloadable IGCSE & GCSE Physics revision notes

The cars in the diagram above have the same speed (a scalar quantity) but different velocities (a vector quantity). Fear not, they are in different lanes!

Examiner Tip

The positive and negative values of velocity can be assigned to any direction as long as the negative velocity is in the opposite direction to the positive value. You can decide which direction you assign to be positive as long as you are consistent throughout a question.

  • The equation for velocity is very similar to the equation for speed:

v equals s over t

  • Where:
    • v = velocity in metres per second (m/s)
    • s = displacement, measured in metres (m)
    • t = time, measured in seconds (s)
  • Velocity is a vector quantity, so it uses displacement, s, which is another vector quantity

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Leander

Author: Leander

Expertise: Physics

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.