Kinematics-linear-motion notes slide show.ppt

kinematics linear motion all notes

1. Describing motion
(along a line)
a.k.a. ‘the kinematics of linear motion’

2. Learning outcomes
•define speed and acceleration, instantaneous and average values
•explain the difference between relevant scalar and vector quantities
•apply Galilean relativity to motions in inertial frames of reference
•present a historical ‘thought experiment’ to illustrate physics thinking
•establish concepts qualitatively (using proportional reasoning) before
introducing quantitative relationships (equations)
•choose contexts for teaching kinematics that motivate student learning
•understand basic algebra and use it to rearrange kinematic equations
•draw and interpret graphs of position, velocity, acceleration
•translate information about uniform motions between words, pictures,
graphs and equations
•begin to develop a strategy for solving quantitative problems

3. Starting points
Misconceptions:
Heavier objects are commonly thought to fall faster than lighter objects.
Teaching challenges:
•Concepts: Some students fail to grasp the distinction between velocity
and acceleration –to them it’s simply ‘motion’. Acceleration is not
simple idea: it is the rate of change of velocity, and velocity itself is the
rate a change of distance (making acceleration the rate of change of a
rate of change).
•Graphs: Most students have difficulty with drawing and interpreting
graphs representing motion (distinguishing s -tgraphs from v -t
graphs; appreciating significance of area under a v -tgraph, of
gradients of s -tand v -tgraphs).
•Equations: Students need help understanding that some equations
constitute definitions and that other equations apply only when there is
constant acceleration.

4. Kinematics –describing motion
Object is treated as a particle(a point-like concentration of
matter that has no size, no shape and no internal structure).
Questions to ask:
•Where is the particle?
•How fast is it moving?
•How rapidly is it speeding up or slowing down?
This is modelling.
Restricted to motion along a line.

5. Contexts
In pairs:
List other examples of real motion that might be
modelled as a particle moving along a line.
•Include some examples that can motivate students.

6. Uniform motion
Galileo (1638) Dialogue concerning two new sciences
Definition:
By steady or uniform motion, I mean one in which the
distances traversed by the moving particle during any
equal intervals of time, are themselves equal.

7. Galileo’sTwo new sciences
Axioms
IThe distance traversed during a _______ interval of time is greater
than the distance travelled during a _______ interval of time.
IIThe time required to traverse a _______ distance is longer than the
time required for a _______ distance.
IIIOver the same time interval, the distance traversed at a greater
speed is _______ than the distance traversed at a ______ speed.
IVThe speed required to traverse a longer distance is greater than
that required to traverse a ________ distance during the same time
interval.

8. Galileo’sTwo new sciences
Theorems
IIf a moving particle, carried at a constant speed, traverses two
distances, the time intervals required are to each other in the
ratio of these distances.
IIIf a moving particle traverses two distances in equal intervals of
time, these distances will bear to each other the same ratio as
the speeds. And conversely, if the distances are as the speeds,
then the times …
IIIIn the case of unequal speeds, the time intervals required to
traverse a given space are to each other inversely as the
speeds.

9. We say …
In symbols, takentime
travelleddistance
speed t
s
v

10. Other essential ingredients
•a coordinate system
•units: metres, seconds
•scalar or vector?
–distance, displacement
–speed, velocity

11. Measuring distances & times
For class experiments & demonstrations
•metre rules and stopwatches
•ticker timers
•light gates
•sonic (ultrasound) sensor
•video capture
Discuss in small groups: What do you use?

12. Graphical representation
Uniform motion
a) List the objects below in order of increasing
speed.
b) Which of the objects have positive velocity?
c) List the objects in order of increasing velocity.

13. Ticker timers
Running on mains, they make 50 ticks each second.
Time between ticks is therefore 1/50 s = 0.02 s

14. A car is driven along a straight road. The graph shows how the
velocity of the car changes from the moment the driver sees a
very slow moving queue of traffic ahead.
Use the graph to calculate the distance the car travels while it is
slowing down.
Show clearly how you work out your answer.
Area under a v-t graph

15. Finding an average speed
1 If you are notalready familiar with ticker timers, first
do the experiment Using the ticker-timer to measure
time
2 Dooneof these two experiments.
Timing a trolley on a slope
Pupil speed

16. Naturally accelerated motion
Aristotle: objects fall at constant speed; the more
massive, the faster they fall.
Galileo’s thought experiment.
(Ignoring air resistance) All objects fall the same way,
getting faster and faster.
•a dramatic experimental test of this idea.
http://www.physics.ucla.edu/demoweb/demomanual/mechanics/gra
vitational_acceleration/guinea_and_feather_tube.html

17. Free fall
Galileo’s findings, modelled with chains.
If the time of fall is twice as long, how much further does
an object fall?
•the v–tgraph gives the answer.
So what happens when an object is thrown vertically
upwards?

18. Graphical representation
Constant acceleration
units: km/h/s, m/s/s or m/s
2t
uv
a

