**1.1 ****
A
few technical terms explained 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^{-1}θ
= 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 /
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.**

INDEX physics notes: Speed
calculations and distance-time
graphs

**
Keywords, phrases and learning objectives for****
speed, motion and graphs**

Know the difference between a scalar quantity like
speed and a vector quantity like velocity.

Know and how to use the technical terms
speed, velocity and displacement

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INDEX physics notes: Speed
calculations and distance-time
graphs