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Magnitudes
Average speeds
Speed ms-1
Light 3x104
Electron around a nucleus
22
Earth around the Sun
1.5
Jet airliner 3x108
Typical car speed 1x10-3
Sprinter 2.5x102
Walking speed 2.2x106
Snail 10
Speed ms-1
Light 3x108
Electron around a nucleus
2.2x106
Earth around the Sun
3x104
Jet airliner 2.5x102
Typical car speed 22
Sprinter 10
Walking speed 1.5
Snail 1x10-3
Acceleration
• When an object's velocity changes, it accelerates.
• Acceleration shows the change in change in velocityvelocity during a period of time.
• Acceleration = change in velocity / time
• ms-2 ms-1 s
“change in velocity”
∆ - this symbol is a Greek (capital) letter, called delta. We use it in physics (and maths) to mean “the change in” a quantity.
∆ - we use it to save us from writing “change in” all the time!
∆ - To calculate the “change in” something we always minus the final quantity from the initial quantity
For example:
• Acceleration = change in velocity / time
..........can written much easier and quicker as:
a = ∆v / t
• A cyclist travels around a circular training track at a constant speed but is considered to be accelerating.
• Discuss!
QUESTION one: If a car accelerates from 5 m/s to 15 m/s in 2 seconds, what is the car's average acceleration?
QUESTION two: How long does it take Kitty to accelerate an object from rest to 10 m/s if the acceleration was 2 m/s2?
QUESTION three: Ella was running at 16m/s on the pavement. She starts to run on the sand and now has a speed of 10m/s. This change in speed took 2 seconds. What is her “acceleration”?
Warm up questions
QUESTION one: If a car accelerates from 5 m/s to 15 m/s in 2 seconds, what is the car's average
acceleration?
Initial velocity = 5 m/sFinal velocity = 15 m/sTime = 2 sa = ? m/s/s
a = ∆v / t = (15 – 5) / 2 = 10 / 2 = 5 m/s/s
How long does it take Kitty to accelerate an object from rest to 10 m/s if the acceleration was 2 m/s2?
Initial velocity = 0 m/sFinal velocity = 10 m/sAcceleration = 2 m/s2
Time = ?s
a = ∆v / t so t = ∆v / a = (10 – 0) / 2 = 10 / 2 = 5s
Clio was running at 16m/s on the pavement. She starts to run on the sand and now has a speed of 10m/s. This change in speed took 2
seconds. What is her “acceleration”?
Initial velocity = 16 m/s Final velocity = 10 m/sTime = 2 s“Acceleration” = ? m/s/s
a = ∆v / t = (10 – 16) / 2= - 6 / 2
= - 3 m/s/sThe minus tells us that it is deceleration!!
Slightly more complex..1. Harriet is riding her bike at 4m/s when she
decides to go a bit faster. She accelerates at 3m/s/s for 5s. What is her final velocity?
2. Tizzy is walking home at 2m/s when she sees the burglar coming out of a house, she gives chase and accelerates at a rate of 2ms-2. If it takes her 4s to accelerate what is her final speed?
3. The burglar has eaten too many pies and cannot accelerate as fast. He goes from stationary to 1m/s in 3s. What is his acceleration?
4. Will Tizzy catch the burglar?
Hattie is riding her bike at 4m/s when she decides to go a bit faster. She accelerates at 3m/s/s for 5s. What is
her final velocity?
Acceleration = 3 m/s/sTime = 5sInitial velocity = 4m/sFinal velocity = ? m/s
a = ∆v / t∆v = a x t = 3 x 5 = 15m/s∆v = final velocity – initial velocity Final velocity = ∆v + initial velocity = 15 m/s + 4= 15 + 4= 19m/s
Tizzy is walking home at 2m/s when she sees the burglar coming out of a house, she gives chase and accelerates at a rate of 2ms-2. If it
takes her 4s to accelerate what is her final speed?
Acceleration = 2 ms-2
Time = 4sInitial velocity = 2m/sFinal velocity = ? m/s
a = ∆v / t∆v = a x t = 2 x 4 = 8ms-1
∆v = final velocity – initial velocity Final velocity = ∆v + initial velocity = 8ms-1 + 2ms-1
= 10ms-1
The burglar has eaten too many pies and cannot accelerate as fast. He goes from stationary to 1m/s in 3s. What is his acceleration?
Acceleration = ? ms-2
Time = 3s
Initial velocity = 0m/s
Final velocity = 1ms-1
a = ∆v / t
a = (1 – 0) / 3
a = 0.3ms-2
Acceleration due to gravity
When objects fall freely through the air on Earth do they fall at
(a)Constant speed
(b)Accelerate at a constant rate
(c) Accelerate at an increasing rate
(d)Decelerate
Acceleration due to gravity
When objects fall freely through the air on Earth they fall at:
(a)Constant speed
(b)Accelerate at a constant rate
At first an object will accelerate at a constant rate and then gradually – as drag builds up, it will fall at a constant speed.
Hand in your homework on GATSOs please!
• Put your name on it!
• TIME TO HAND OUT BOOKS!
Task
• In groups of 3 use A3 paper to draw a diagram of a sky diver jumping out of a plane and falling.
• Include all stages of the fall until he lands – his parachute works.
• Include all force arrows, forms of motion and whether forces are balanced or unbalanced:
You have 5minutes
Uniformly accelerated motion in a straight line
• The melon clip:
• http://clipbank/espresso/clipbank/servlet/asset?assetID=5062
• The not so alive parachutist clip:
• http://clipbank/espresso/clipbank/servlet/asset?assetID=4450
Task
• Complete question on parachutist
• Homework: the rest of this sheet is to be completed for homework: Due in on Tuesday
Uniformly accelerated motion in a straight line
• There are 4 equations known as the “kinematic equations” or “equations of motion” that will completely describe the motion of a particle if it is travelling in a straight line and with uniform motion:
• You need to know where they come from as well as being able to use them!
• The equations of motion are valid only when acceleration is constant and motion is constrained to a straight line.
• We are over simplifying reality with a model so that we can an idea of the actual value.
What are the symbols and variables involved?
• s Displacement (m)
• u Initial velocity (ms-1)
• v Final velocity (ms-1)
• a Acceleration (ms-2)
• t Time (s)
Deriving the equations (There are 4 of them)
• You know the first one already but now it is written with v (final velocity) as the subject of the equation.
• a = v – u / t now written as
• v = u + at EQUATION ONE
Equation TWO: What is the displacement of this object?
• Note: v = u + at so v – u = at
Time (s)
Velocity (ms-1)
The area below the line of this graph tells you the displacement of the object:
Area of triangle: (v – u) x t / 2
Area of rectangle: ut
Total area: rectangle + triangle
= ut + (v-u)t / 2
= ut + at x t / 2
= ut + ½ at2
V
U
t
Equation Two
s = ut + ½at2
Equations so far:
v = u + at
s = ut + ½at2
Equation Three: What is the displacement, s of this object?
Time (s)
Velocity (ms-1)
The area below the line of this graph tells you the displacement of the object:
Total area: rectangle + triangle
s = ut + (v-u) ½ t
MULTIPLE OUT THE BRACKETS!
V
U
t
ut + (v-u) ½ t
ut + ½ vt - ½ ut
ut - ½ ut = ½ ut
½ vt + ½ ut Factorise:
½ t (v + u)
Equation Three
s = ½ t (v + u)
Equations so far:
v = u + ats = ut + ½at2
s = ½ t (v + u)
Equation 4:
• All three equations so far have t in them - it would be useful to get rid of it.
• Starting with the first equation, v = u + at we can write:
t = (v-u)÷a
This can be substituted into
the third, s = ½ (u+v) t :
s = ½ (u+v) (v-u)÷a
s = ½ (u+v) (v-u)÷a
• Expanding the brackets, and multiplying out the ½ and a:
2as = (u+v)(v-u)
uv - u2 + v2 + uv
2as = v² - u²
• This rearranges to: v² = u² + 2as
4 Equations of Motion
v = u + ats = ut + ½at2
s = ½ t (v + u) v² = u² + 2as
Example:
A car is travelling at 15ms-1 when it breaks and takes 50m to stop. Calculate the deceleration of the car.
s = 50m
u = 15ms-1
v = 0ms-1
a = ?ms-2
t = ?s
Which equation should you use?
HINT:
It has to be one without t in it!!!
4 Equations of Motion
v = u + ats = ut + ½at2
s = ½ t (v + u) v² = u² + 2as
v² = u² + 2as
A car is travelling at 15ms-1 when it breaks and takes 50m to stop. Calculate the deceleration of the car.
s = 50m
u = 15ms-1
v = 0ms-1
a = ?ms-2
t = ?s
Re arrange first:
v² = u² + 2as
a = (v² - u² ) / 2s
a = (0 – 152) / (2 x 50)
a = - 225 / 100
a = -2.25ms-2
Your turn:
• You MUST write down your answers to all questions using the format provided.
• Complete q1 – 7 (you might recognise q2!)
• Finish for homework