Defining displacement, velocity & acceleration
Distance and displacement
Distance
- Distance is a measure of how far an object travels
- It is a scalar quantity with magnitude only
Total running distance
The athletes run a total distance of 300 m
- Consider some athletes running a 300 m race on a 400 m track
- The distance travelled by the athletes is 300 m
Displacement
- Displacement is a measure of how far something is from its starting position, along with its direction
- In other words, it is the change in position
- It is a vector quantity with both magnitude and direction
Total distance vs total displacement
The athletes run a total distance of 300 m, but end up 100 m from where they started
- Consider the same 300 m race again
- The athletes have still run a total distance of 300 m (this is indicated by the arrow in red)
- However, their displacement at the end of the race is 100 m to the right (this is indicated by the arrow in green)
- If they had run the full 400 m, their final displacement would be zero
- Distance is a scalar quantity because...
It describes how far an object has travelled overall, but not the direction it has travelled in
- Displacement is a vector quantity because...
It describes how far an object is from where it started and in what direction
Speed and velocity
Speed
- The speed of an object is the distance it travels every second
- Speed is a scalar quantity with magnitude only
- The average speed of an object is given by the equation:
- The SI units for speed are meters per second (m s−1) but speed can often be measured in alternative units e.g. km h−1 or mph, when it is more appropriate for the situation
Velocity
- The velocity of a moving object is similar to its speed and also describes the direction of the velocity
- Velocity is defined as:
The rate of change of displacement
- Velocity is, therefore, a vector quantity because it describes both magnitude and direction
- Velocity is the speed in a given direction
- The average velocity of an object can be calculated using
- Where:
- = total displacement, or change in position, measured in (m)
- = total time taken, measured in (s)
- If the initial velocity u and final velocity v are known, the average velocity can also be calculated using:
Examiner Tip
Velocity is speed in a given direction, but average velocity is not average speed in a given direction. This is because speed uses distance, and velocity uses displacement, and the magnitudes of these values can be very different for the same motion.
Acceleration
- Acceleration is defined as:
The rate of change of velocity
- Acceleration is a vector quantity and is measured in metres per second squared (m s–2)
- It describes how much an object's velocity changes every second
- The average acceleration of an object can be calculated using:
- Where:
- = average acceleration, measured in m s–2
- = change in velocity, measured in m s–1
- = total time taken, measured in s
- The change in velocity is the difference between the initial and final velocity, as written below:
change in velocity = final velocity − initial velocity
Worked example
A professor walks around her garden following the path ABCDA.
Calculate, at the end of their walk
Answer:
(a) The distance the professor travels is:
- The total distance of each side of the rectangle
15 + 9 + 15 + 9 = 48 km
(b) The displacement of the professor is:
- The displacement is how far the professor is from their original position
- As they travel back to point A, the total displacement = 0 km