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Kinematics : Describing Motion - Coggle Diagram
Kinematics
:
Describing Motion
Displacement-Time Graphs
Steeper slope = greater velocity
Negative gradient = negative velocity (moving backwards)
Gradient (slope) equals velocity
Deducing velocity
Calculate gradient of graph*
(Δs / Δt)*
Example
:
Toy car, initial steady velocity, then stops
Plot data
(displacement vs time)
Represents changing position
Scalar and Vector Quantitites
Scalar Examples
Density
Work (add regardless of opposing forces)
Mass
Pressure
Time (total time adds regardless of direction)
Vector examples
Force (opposing forces cancel)
Acceleration
Combining Velocities
Example
Swimming across a river (swimming velocity + current velocity)
Resultant will be diagonal
Velocity is a Vector, combines by vector addition
Calculating Resultant Velocity
Join start and end points
Use Pythagora's theorem (if 90)
Sketch vector triangle (head-to-tail)
Calculate magnitude and direction (angle)
Sketch diagram
Example
Aircraft with side wind
Speed
Units
SI System
metres :
(m)
, seconds :
(s)
Speed Unit
m s-1 (m/s)
Other Units
km s-1
km h-1 (km/h)
cm s-1
mph
Determining Speed (Laboratory Methods)
General
which is
Time travel between two fixed points
only gives average speed
Methods for Trolley
One Light Gates
Trailing edge passes
:
timer stops
Time
:
time travel length of card
Leading edge breaks beams
:
timer starts
Computer calculates speed directly
Ticker-Timer
Interpreting Tapes
Even spacing
:
constant speed
Increasing Spacing
:
Increasing Speed
Measure of every fifth dot
Patterns of dots records movement
Draw distance-time graph
Mark dots at regular intervals
Two Light Gates
Card breaks first beam
:
time starts
Card breaks second beam
:
timer stops
Speed
=
distance between gates/time interval
Motion Sensor
Computer deduces distance to trolley
Generates distance-time graph
Detects reflected waves, determines travel time
Speed determine from graph
Transmits ultrasound pulses
Calculation
Constant Speed
Average Speed
: Distance/Time
(v = d/t)
Instantanenous Speed
if (example)
you look at the speedometer in a car, it doesn’t tell you the car’s average speed; rather, it tells you its
speed at the instant when you look at it.
Distance and Displacement, Scalar and Vector
Distance
Scalar Quantity (magnitude only)
Scalar Quantity
Had magnitude only
Examples : distance, speed, mass, time, density, work, pressure
Displacement
example : 15 km walked, displacement at 030
Vector Quantity (magnitude and direction)
Distance travelled in a particular direction
Vector Quantity
Has both magnitude and direction
Examples : displacement, velocity, force, acceleration
Speed and Velocity
Velocity
Vectro quantity
Defined as displacement / time (v = Δs / Δt)
Speed in particular direction
Rate of change of displacement
Speed
Scalar quantity
(no direction)
Standard Symbols and Units
Displacement
:
s, x, m
Time
:
t, s
Distance
:
d, m
Speed, Velocity
:
v, m s-2
Calculations
Importance of units (SI units preferred, but non-SI possible if consistent
Worked examples : car travel, light from sun, spacecraft
Rearranging Equations (s = vt, t = s/v*
Combining Displacements (vector Addition)
Combined effect is resultant
Methods
theare are 3, which is
Pythagoras's Theorem
Example
:
Spider on table (OA, AB)
Calculate magnitude and direction (angle 0)
For displacements at right angles
Scale drawing
Draw vectors head-to-tail
Join start to finish (resultant vector)
Choose suitable scale
Measure length and angle of resultant
For displacement not at 90 degrees
Example
: **Air craft flight (east, then north-east)
Adding two or more vectros
Subtracting Vectors
Key Idea
Add the negative vector
Negative of a Vector : same size, opposite direction
Formula
: A-B = A + (-B)
Cases
Opposite direction : 10 m/s N - 4 m/s S = 14 m/s N (add 4 m/s N)
Different direction : use diagram (A + (- B))
same direction : 10 m/s N - 4 m/s N + 6 m/s N (add 4 m/s S)