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~