Physics - Mechanics - Accelerated motion

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Chapter 2: Accelerated motion
What is acceleration and how is it calculated?
Acceleration is the rate of change of velocity with respect to time
Because velocity is a vector quantity it also means that acceleration is a vector quantity
If an object is moving with constant speed but is changing direction, it is accelerating
It is calculated using the word equation:
Acceleration (m/s^2) = change in velocity (m/s) / time taken (s)
The change in velocity is calculated by (v ­ u)
Acceleration = (v ­ u) / t
Deducing acceleration
A straight line with a positive slope shows constant acceleration
The greater the slope, the greater the acceleration
The velocity is constant, so there is no acceleration
A negative slope shows deceleration
The slope is changing; the acceleration is changing
Using the graph we can just calculate the gradient:
dy/dx = dv/dt

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Deducing displacement
Simply work out the area underneath the graph to work out the displacement of the object
For curved graphs you can just count the squares or integrate
Determining velocity and acceleration in the laboratory
One light gate (method 1)
Attach a bit of card to the object (in the shape of two towers)
A computer records the time of the first interruption and the second (t2 ­ t1 and t4 ­ t3)
Initial velocity = l1 / (t2 ­ t1) and the final…read more

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Equation 1: v = u + at
Equation 2: s = (u +v)t / 2
Equation 3: s = ut + (at^2)/2
Equation 4: v^2 = u^2 + 2as
Equation 5: s = vt ­ (at^2)/2…read more

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Deriving the equations of motion
Equation 1: derived directly from the acceleration equation
Equation 2: derived directly from the average speed equation, where (u + v)/2 = average speed
Equation 3: Using the area underneath the graph we can work the out the sum of the displacements
Equation 4: derived directly from equations 1 and 2
Equation 5: derived in the exact same way as equation 3
Uniform and non-uniform acceleration
The equations of motion only apply to objects moving with a constant acceleration
Constant…read more


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