Speed & Velocity (Cambridge (CIE) IGCSE Physics)

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:

• Where:

  • = speed, measured in metres per second (m/s)

  • = distance travelled, measured in metres (m)

  • = 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

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 speed considers the total distance travelled and the total time taken

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:

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

Velocity

• 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

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!

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

• 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