1.1 A few technical terms explained involving speed and velocity

Defining and explaining technical terms like scalar quantity, vector quantity, displacement, involving speed and velocity

How do you calculate speed or velocity?

What is the difference between scalar and vector quantities in motion?

What is the difference and similarity between speed and velocity?

A scalar quantity only has a magnitude and no specified direction

e.g. distance, energy, mass, speed (without change in direction), temperature, time etc.

A vector quantity has both magnitude (size) and specified direction

e.g. acceleration, displacement, force, momentum, velocity, weight etc.

When talking about vectors, you should appreciate that their values can be positive and negative.

A car might have a speed of 10 m/s, but its velocity might be 10 m/s in one direction, but if it changes direction by 180^o, keeping the same speed, its velocity will be considered to be -10 m/s.

It is possible to have an object moving with a constant speed, but its velocity changes.

e.g. if an object is moving in a circle at constant speed, the velocity is constantly changing, because the direction of motion is constantly changing even though the speed may be constant..

Distance:

Distance is how far an object has moved in any direction, the direction isn't specified, so its a scalar measurement.

e.g. a car moves 30 km, a ball is tossed in the air to a height of 3 m.

Displacement:

What do we mean by displacement?

Displacement is how far an object has been moved in a straight line from specified starting point to a specified finishing point, but in particular specified direction/directions, so its a vector measurement.

It does not necessarily mean the object has moved in a straight line - it may or may not.

Examples of displacements

(i) an object moves 1300 km north, displacement = 1300 km

(ii) an object moves 300 m north and 400 m east, displacement is 500 m north-east bearing 59^o from north)

(Draw this for your self and measure the angle, or calculate it, Tan θ = (400/300) = 1.333, Tan^-1θ = 59^o)

(iii) an object moves 3 m east and 3 m west, displacement is 0 m, because object has returned to its starting point.

However, the object has moved a distance of 6 m in total, and you can consider it does two 3 m displacements, but take in expressing the situation!

For a similar argument think of an object that moves once in a circular path of circumference 6 m.

The total distance travelled is 6 m, but the displacement is zero, because the object ends up where it started.

 

Speed:

Speed is how fast an object is moving but no direction is specified, so its a scalar measurement.

So speed has magnitude but no direction is indicated.

speed = distance travelled / time taken

e.g. a car travelling at 30 m/s or a train travelling at 200 km/hour, but real journeys obviously involve regularly changing direction and speed - so strictly speaking, many changes in velocity (see next).

In these examples, because the speed is variable, can calculate the 'average speed'.

average speed = total distance travelled / total time taken

To measure the constant speed of an object need some means of measuring time (stopwatch) and distance (tape measure). Speed/velocity calculations explained in the next section.

 

Velocity

Velocity is how fast an object is travelling in a particular direction, so its a vector measurement.

The formula for velocity is still

distance travelled (displaced) in a straight line / time taken

So velocity has magnitude and a specified direction.

e.g. a plane moving at a constant speed of 600 km/hour at 50^o from due north.

Two cars, travelling at identical speeds, passing in opposite directions have different velocities - different directions.

You can having objects moving at a constant speed but continually changing velocity.

e.g. any object moving in a circle at constant speed is continuously changing velocity because it is continually changing direction. Whirling an object around on the end of string is a simple example.

Both speed and velocity tell you how fast an object is moving.