Speed & Velocity (Oxford AQA IGCSE Physics)
Revision Note
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
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:
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
Multiply both sides by t, then put displacement on the left
Step 4: Substitute in the known values to calculate
Examiner 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
This equation for average speed is an adapted form of the velocity equation
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
1 minute = 60 s
Step 3: Write out the average speed equation
Step 4: Substitute the known values to calculate
Examiner 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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