Speed and Velocity

Speed

In the BGE Science course, as well as S1-2 Maths courses, the concept of Speed was covered. Speed is a measure of how fast an object is moving. The Speed of an object can be found using the following formula:-

As can be seen from the above box, there are two different ways to describe Speed within Physics:-

Average Speed - measured over a long time - It is measured over a whole journey and is found using the distance travelled overall and the time taken.

Instantaneous Speed - measured over a very short time - It is the object's Speed at that instant.


Measuring Average Speed Experimentally

The diagram below shows the class-based experimental set-up for the measurement of average speed:-

By measuring the length of the ramp (in meters) and the time taken to travel the length of the ramp (in seconds), the average Speed can be found using the above formula.


Measuring Instantaneous Speed Experimentally

The diagram below shows the class-based experimental set-up for the measurement of Instantaneous speed:-

By measuring the length of the single mask (in meters) and the time taken to break the beam (in seconds), the Instantaneous speed at the bottom of the ramp can be found using the above formula.


Speed and Velocity

As stated earlier, there is a difference between Speed and Velocity. In order to calculate these, a variation on the above formula should be used:-

For speed:-

Speed = Distance / time or s = d / t

For Velocity

Velocity = Displacement / time or v = s / t

Note - the two different meanings of 's' :-

In Speed formula - 's' is Speed.

In Velocity formula - 's' is Displacement.

Example 1 -

A plane flies due north for 200 km, taking 30 minutes. The plane experiences a cross-wind blowing due east at 50 ms-1. What is the resultant Velocity of the plane?

VNorth = 200,000 / ( 30 x 60 )

= 111 ms-1

VEast = 50 ms-1

Resultant Velocity = square root (1112 + 502)

= 122 ms-1

Tan (θ) = 50 / 111

θ = 24°

The resultant Velocity of the aircraft is 122 ms-1 at a bearing of 024.


Example 2 -

If an orienteer travels between the three checkpoints as shown below, what is their:-

1. Distance travelled.

2. Displacement.


And If AB takes 20 minutes and BC takes 15 minutes, what is their :-

3. Average Speed.

4. Velocity.

Displacement =

Distance travelled = 2.3 + 0.8

Displacement travelled = 3.1 km


Displacement = square root (2.32 + 0.82)

Displacement = 2.4 km

Tan (θ) = 0.8 / 2.3

θ = 19°

Displacement = 2.4 km at a bearing of 251 (or 2.4 km at an angle of 19° South of West).


Average Speed = Distance / Time

Average Speed = 3.1x103 / (35 x 60)

Average Speed = 1.5 ms-1


Velocity = Displacement / Time

Velocity = 2.4x103 / ( 35 x60 )

Velocity = 1.1 ms-1

Velocity = 1.1 ms-1 at a bearing of 251 (or 1.1ms-1 at an angle of 19° South of West).