Speed & Velocity (Cambridge (CIE) IGCSE Physics): Revision Note

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:

$v=\frac{s}{t}$

• 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

• Average walking speed = 1.5 m/s

• Average running speed = 3 m/s

• Average cycling speed = 6 m/s

An experienced 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 

• A car travels at different instantaneous speeds throughout its journey

  • The car speeds up and slows down

  • The car may stop at junctions and traffic lights

• The average speed of the journey of the car can be found by dividing the total distance travelled by the total time taken

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

 $\mathrm{Average}\mathrm{speed}=\frac{\mathrm{total}\mathrm{distance}\mathrm{travelled}}{\mathrm{total}\mathrm{time}\mathrm{taken}}$

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

Formula triangle for average speed, distance travelled and time taken

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

The cars in the diagram above have the same speed (a scalar quantity) but different velocities (a vector quantity).

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

$v=\frac{s}{t}$

• Where:

  • $v$ = velocity, measured 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

• When dealing with velocities, direction must be stated alongside the answer