Mechanics Chapter 2 :: �Variable Acceleration
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Functions of time
Up to now, the acceleration has always been constant in any particular period of time…
constant deceleration
no acceleration
constant acceleration
time
velocity
time
velocity
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b
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2
6
24
(4,-8)
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b
c
d
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Exercise 2A
Pearson Mechanics 2
Page 27
Using Differentiation
and similarly…
velocity is the rate of change of displacement
acceleration is the rate of change of velocity
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a
b
c
Test Your Understanding
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b
c
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Exercise 2B
Pearson Mechanics 2
Page 30-32
Maxima and Minima Problems
a
b
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Test Your Understanding
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a
b
Edexcel M2 June 2013 Q3a,b
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a
b
Exercise 2C
Pearson Mechanics
Page 34-36
Using Integration
Differentiating (with respect to time) gets us from displacement to velocity, and from velocity to acceleration.
So naturally, integrating (with respect to time) gets us from acceleration to velocity, and from velocity to displacement. As mentioned earlier, it’s helpful to picture the graph on the left, where we move down to differentiate and up to integrate.
Recall in Pure Year 1 that we can find the constant of integration by using known values.
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b
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Further Example
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Further Example
Edexcel M2 June 2015 Q6
a
b
c
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Exercise 2D
Pearson Mechanics 2
Page 38-39
Constant acceleration formulae
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a
b
Exercise 2E/2F
Pearson Mechanics 2
Pages 42-43
The End