Transcript velocity &displacement

Dynamics and Space
Velocity and displacement
Vectors and scalars
Learning Outcomes
• Vector and scalar quantities: force, speed,
velocity, distance, displacement, acceleration,
mass, time and energy.
• Calculation of the resultant of two vector
quantities in one dimension or at right angles.
• Determination of displacement and/or
distance using scale diagram or calculation
• Use of appropriate relationships to calculate
velocity in one direction.
Lesson 1
1. Define what is meant by vector and
scalar quantities.
2. Describe the difference between
distance and displacement and speed
and velocity.
3. Calculate the resultant of two vector
quantities at right angles to one
another.
Scalar And Vector Quantities
All physical quantities can be divided into two
groups – vectors or scalars.
When determining if a quantity is a vector or
a scalar you need only ask one question, does
direction matter?
• A scalar quantity has size (magnitude) only.
• A vector quantity has both size and direction.
Distance and Displacement
• Distance, d, is how far an object has travelled
between two points, regardless of direction.
• It is a scalar and is measured in metres.
• Displacement, s, is the shortest distance
travelled between two points in a straight
line.
• It is a vector measured in metres and in a
particular direction.
Speed and Velocity
•
Speed and velocity can be calculated by using the following equations:
•
Speed = distance
time
velocity = displacement
time
where speed is a scalar and velocity is a vector.
•
The direction of the velocity will be the same as that calculated for
displacement.
Example 1
•
A boy walks 40 m north, then
turns back south for 10 m. The
journey takes 20 seconds.
What is
a)
b)
c)
d)
the displacement of the boy
the distance the boy travelled
the average velocity
the average speed
a) s = 40–10 = 30 m
north
b) d = 40 + 10 = 50 m
c) v = s / t = 30 / 20
= 1.5 m/s north
d) v = d / t = 50 / 20
= 2.5 m/s
Example 2
•
A car drives 60 km north, then
80 km east, as shown in the
diagram. The journey takes 2
hours. Calculate (in km or
km/h):
a)
b)
c)
d)
the distance travelled
the displacement
the average speed
the average velocity
a) d = 80 + 60 = 140 km
b) s2 = 802 + 602
s = 100 km
tan Θ = 80 / 60
Θ = 530 W of N /
(053)
c) v = d / t = 140 / 2
= 70 km/h
d) v = s / t = 100 / 2
= 50 km/h (053)
NB: The method used for part b) can also be used to
work out resultant forces at right angles.
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Lesson 2
1. Define what is meant by vector and
scalar quantities.
2. Investigate different quantities to
determine if they are vector or scalar.
3. Identify vector quantities and scalar
quantities.
Experiment
• You can now carry
out experiments to
determine if the
following quantities
are vectors or
scalars:
Vector or scalar?
Quantity
Mass
Force
Acceleration
Time
Energy
Prediction Observation
Examples of Vectors and Scalars
Vectors
Scalars
Velocity
Displacement
Acceleration
Force
Speed
Distance
Mass
Time
Energy (all types)
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Lesson 3
1. Describe how to measure the average
speed of an object.
2. Carry out calculations on the above.
Average Speed
•
The average speed of a body is
found by dividing the total distance
travelled by the time of the whole
journey.
v
=
d
t
Experiment
•
Measure out a distance and record the time
taken to travel that distance. Use the results
obtained to calculate your average speed in the
table below.
Task
Walking
Your choice from:
Running / hopping /
backwards walk etc
Distance
Time
covered (m) taken
(s)
Average
speed (m/s)
How to measure average
speed
(3 marks)
1. Measure out a distance (½) using a
ruler (½) .
2. Record the time taken to travel the
distance (½) using a stopwatch (½).
3. Use the equation:
v
=
d
t
(1)
2005 Qu: 21
Thinker
Do you know your average speeds?
Lesson 4
1. Describe how to measure the
instantaneous speed of an object.
2. Carry out calculations on the above.
Instantaneous Speed
•
•
•
Instantaneous speed is the speed of
an object at a particular instance in
time.
It is also calculated using v = d / t.
The instantaneous speed is
measured over a very small distance
and time period.
Experiment
Measuring Instantaneous
Speed
1. Record the length of the mask on
the trolley, d, in metres.
2. Release trolley down slope.
3. Trolley cuts light gate which then
allows the electronic timer to
record time, t, in seconds.
4. Instantaneous speed, v, is calculated
using v = d / t.
Experiment
Length of mask =
Distance up
slope (m)
0.25
0.50
0.75
1.00
m
Time taken for mask Instantaneous
to pass through light speed (m/s)
gate (s)
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2004 Qu:21
Summary
Velocity and displacement
You should now be able to do the following:
• Identify vector and scalar quantities from the following:
force, speed, velocity, distance, displacement, acceleration,
mass, time and energy.
• Calculate the resultant of two vector quantities in one
dimension or at right angles.
• Determine the displacement and/or distance using scale
diagram or calculation.
• Use of appropriate relationships to calculate velocity in one
direction.