Motio n © David Hoult 2009
Motion © David Hoult 2009. Displacement is distance moved in a specified direction © David Hoult 2009.
Dec 25, 2015
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Motion
© David Hoult 2009
Displacement is distance moved in a specified direction
© David Hoult 2009
Displacement is therefore a vector quantity
Displacement is distance moved in a specified direction
© David Hoult 2009
S I unit of displacement is the meter, m
Displacement is therefore a vector quantity
Displacement is distance moved in a specified direction
© David Hoult 2009
“S I” - système international d'unités… the modern system based on the three fundamental units:
Meter for distance
© David Hoult 2009
“S I” - système international d'unités… the modern system based on the three fundamental units:
Meter for distance
Second for time
© David Hoult 2009
“S I” - système international d'unités… the modern system based on the three fundamental units:
Meter for distance
Second for time
Kilogram for mass
© David Hoult 2009
All other units (for force, electric current, energy etc) are called derived units and are based on the three fundamental units of mass, distance and time.
© David Hoult 2009
Speed is distance moved per unit time
© David Hoult 2009
Speed is distance moved per unit time
When stating a speed, no direction needs to be given because speed is a scalar quantity.
© David Hoult 2009
Speed is distance moved per unit time
When stating a speed, no direction needs to be given because speed is a scalar quantity.
The units of speed are meters per second, ms-1
© David Hoult 2009
Velocity is distance moved per unit time in a specified direction (and sense)
© David Hoult 2009
Velocity is distance moved per unit time in a specified direction (and sense)
Velocity is therefore a vector quantity
© David Hoult 2009
The units of velocity are meters per second, ms-1
Velocity is distance moved per unit time in a specified direction (and sense)
Velocity is therefore a vector quantity
© David Hoult 2009
Acceleration is the rate of change of velocity
© David Hoult 2009
Acceleration is the rate of change of velocity
Acceleration is therefore a vector quantity
© David Hoult 2009
Acceleration is the rate of change of velocity
Acceleration is therefore a vector quantity
© David Hoult 2009
Acceleration is the rate of change of velocity
Acceleration is therefore a vector quantity
© David Hoult 2009
Acceleration is the rate of change of velocity
Acceleration is therefore a vector quantity
If the change took 20 seconds and was uniform then the speed (or velocity) changed by
© David Hoult 2009
Acceleration is the rate of change of velocity
Acceleration is therefore a vector quantity
If the change took 20 seconds and was uniform then the speed (or velocity) changed by
5 meters per second each second© David Hoult 2009
The units of acceleration are meters per second per second, ms-2
© David Hoult 2009
Using Graphs to represent Motion
© David Hoult 2009
© David Hoult 2009
© David Hoult 2009
Stationary body © David Hoult 2009
Stationary body © David Hoult 2009
© David Hoult 2009
Body moving with uniform velocity © David Hoult 2009
Body moving with uniform velocity © David Hoult 2009
Body moving with uniform velocity in the negative sense © David Hoult 2009
A
B
© David Hoult 2009
Body B moving faster than body A
A
B
© David Hoult 2009
The slope of a displacement / time graph gives the magnitude and sense of the velocity of the body
© David Hoult 2009
Body accelerating © David Hoult 2009
If the acceleration is uniform the curve is a parabola © David Hoult 2009
Body accelerating © David Hoult 2009
Body accelerating in the negative sense © David Hoult 2009
© David Hoult 2009
© David Hoult 2009
Uniform velocity © David Hoult 2009
Uniform velocity in the negative sense © David Hoult 2009
© David Hoult 2009
Stationary body © David Hoult 2009
Body B moving faster than body A © David Hoult 2009
Body B moving faster than body A © David Hoult 2009
Body B moving faster than body A
A
B
© David Hoult 2009
Body accelerating uniformly © David Hoult 2009
Body accelerating uniformly © David Hoult 2009
Body accelerating uniformly in the negative sense © David Hoult 2009
The slope of a velocity / time graph gives the magnitude and sense of the acceleration of the
body
© David Hoult 2009
Using a velocity / time graph to find displacement
© David Hoult 2009
Using a velocity / time graph to find displacement
© David Hoult 2009
Using a velocity / time graph to find displacement
© David Hoult 2009
Using a velocity / time graph to find displacement
In 8 seconds, the body moves 10 × 8 = 80 m
© David Hoult 2009
Using a velocity / time graph to find displacement
© David Hoult 2009
Using a velocity / time graph to find displacement
The calculation of the displacement of the body is the same as calculating the area under the graph between 0 and 8 seconds © David Hoult 2009
The area under a velocity / time graph represents the displacement of the body
© David Hoult 2009
Equations of Motion
© David Hoult 2009
These equations are useful when bodies move with uniform acceleration.
Symbols used in the equations:
© David Hoult 2009
These equations are useful when bodies move with uniform acceleration.
t represents time
Symbols used in the equations:
© David Hoult 2009
These equations are useful when bodies move with uniform acceleration.
Symbols used in the equations:
t represents time
a represents acceleration
© David Hoult 2009
These equations are useful when bodies move with uniform acceleration.
Symbols used in the equations:
t represents time
a represents acceleration
u represents “initial” velocity (or speed)
© David Hoult 2009
u represents “initial” velocity (or speed)
These equations are useful when bodies move with uniform acceleration.
Symbols used in the equations:
t represents time
a represents acceleration
v represents “final” velocity (or speed)
© David Hoult 2009
These equations are useful when bodies move with uniform acceleration.
t represents time
Symbols used in the equations:
a represents acceleration
u represents “initial” velocity (or speed)
v represents “final” velocity (or speed)
s represents the displacement of the body from a reference point (usually the position of the body at t = 0)
© David Hoult 2009
The average speed of a body can always be found using
© David Hoult 2009
The average speed of a body can always be found using
taken time
moved distancevav
© David Hoult 2009
If the speed of a body changes from u to v and the acceleration is uniform
© David Hoult 2009
If the speed of a body changes from u to v and the acceleration is uniform
© David Hoult 2009
If the speed of a body changes from u to v and the acceleration is uniform
© David Hoult 2009
If the speed of a body changes from u to v and the acceleration is uniform
In this case the average speed is 2
uv © David Hoult 2009
Therefore, to calculate the displacement of a body at time t, we might use
© David Hoult 2009
Therefore, to calculate the displacement of a body at time t, we might use
t2
uvs
equation 1
© David Hoult 2009
From the definition of acceleration we have
t
uva
© David Hoult 2009
From the definition of acceleration we have
t
uva
This equation is often rearranged to allow us to find the speed (or velocity) of a body after a period of acceleration
© David Hoult 2009
From the definition of acceleration we have
t
uva
This equation is often rearranged to allow us to find the speed (or velocity) of a body after a period of acceleration
v = u + at equation 2
© David Hoult 2009
Combining equations 1 and 2 in order to eliminate v gives
© David Hoult 2009
Combining equations 1 and 2 in order to eliminate v gives
s = u t + ½ a t2 equation 3
© David Hoult 2009
Combining equations 1 and 2 in order to eliminate v gives
s = u t + ½ a t2 equation 3
Combining equations 2 and 3 in order to eliminate t gives
© David Hoult 2009
Combining equations 1 and 2 in order to eliminate v gives
s = u t + ½ a t2 equation 3
v2 = u2 + 2 a s equation 4
Combining equations 2 and 3 in order to eliminate t gives
© David Hoult 2009
The Acceleration due to Gravity (g)
(also called Acceleration of Free Fall)
© David Hoult 2009
The Acceleration due to Gravity (g)
(also called Acceleration of Free Fall)
Experiments show that all bodies fall with the same acceleration
© David Hoult 2009
The Acceleration due to Gravity (g)
(also called Acceleration of Free Fall)
Experiments show that all bodies fall with the same acceleration as long as air resistance is negligible.
© David Hoult 2009
Experiments show that all bodies fall with the same acceleration as long as air resistance is negligible.
g (in Paris) is about 9.8 ms-2
The Acceleration due to Gravity (g)
(also called Acceleration of Free Fall)
© David Hoult 2009
The value of g is not the same at all points on the Earth.
© David Hoult 2009
The value of g is not the same at all points on the Earth.
The value of g is affected by:
© David Hoult 2009
The value of g is not the same at all points on the Earth.
The value of g is affected by:
i) altitude
© David Hoult 2009
The value of g is not the same at all points on the Earth.
The value of g is affected by:
i) altitude
© David Hoult 2009
The value of g is not the same at all points on the Earth.
The value of g is affected by:
i) altitude
ii) latitude
© David Hoult 2009
The value of g is not the same at all points on the Earth.
The value of g is affected by:
i) altitude
ii) latitude; the Earth is not a perfect sphere
© David Hoult 2009
The value of g is not the same at all points on the Earth.
The value of g is affected by:
i) altitude
ii) latitude; the Earth is not a perfect sphere
iii) the rotation of the Earth
© David Hoult 2009
The value of g is not the same at all points on the Earth.
The value of g is affected by:
i) altitude
ii) latitude; the Earth is not a perfect sphere
iii) the rotation of the Earth
The value of g is less than it would be if the earth did not rotate.
© David Hoult 2009
The value of g is not the same at all points on the Earth.
The value of g is affected by:
i) altitude
ii) latitude; the Earth is not a perfect sphere
iii) the rotation of the Earth
The value of g is less than it would be if the earth did not rotate.
The value of g is affected most at places where the speed of circular motion is greatest, that is, on the equator © David Hoult 2009
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