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

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

Speed-time graphs

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.

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:

rearranging

rearranging

subtracting these two equations to eliminate *v*

it is left to the reader to show that :

hint: try multiplying the two equations instead of subtracting

In A2/A-Level Mathematics, summary:

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