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A2/A-level Mathematics: Uniform Acceleration --- Part 1

Uniform Acceleration

· mathematics,A2 Mathematics,alevel mathematics,uniform acceleration

In A2/A-Level Mathematics, to understand this section you must remember the letters representing the variables:

u - initial speed

v - final speed

a - acceleration(+) or deceleration(-)

t - time taken for the change

s - displacement(distance moved)

It is also important to know the S.I. units ( Le Système International d'Unités) for these quantities:

u - metres per second (ms-1)

v - metres per second (ms-1)

a - metres per second per second (ms-2)

t - seconds (s)

s - metres (m)

in some text books 'speed' is replaced with 'velocity'. Velocity is more appropriate when direction is important.

Displacement-time graphs

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In A2/A-Level Mathematics, for a displacement-time graph, the gradient at a point is equal to the speed .

Speed-time graphs

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For a speed-time graph, the area under the curve is the distance travelled. The gradient at any point on the curve equals the acceleration.

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In A2/A-Level Mathematics, Note, the acceleration is also the second derivative of a speed-time function.

Equations of Motion

One of the equations of motion stems from the definition of acceleration:

acceleration = the rate of change of speed

a = (v-u) / t

rearranging

v= u + at

if we define the distance 's' as the average speed times the time(t), then:

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rearranging

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rearranging

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subtracting these two equations to eliminate v

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it is left to the reader to show that :

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hint: try multiplying the two equations instead of subtracting

In A2/A-Level Mathematics, summary:

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That's end of Part 1. Now you can proceed to Part 2~

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