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 180o, 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 59o from north)
(Draw this for your self and measure
the angle, or calculate it, Tan θ = (400/300) = 1.333, Tan-1θ
= 59o)
(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 50o 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
