II Speed, Velocity, Acceleration

Speed

Measure of how much distance is passed per time taken.

Unit Speed

$m/s$ or $ms^{-1}$

Constant Speed

$\text{distance} = \text{speed} \times \text{time taken}$

Varying Speed

$\text{Average speed} = \frac{\text{Distance travelled}}{\text{Time taken}}$

Equations and Symbols

$s = \text{distance moved}$
$v = speed$
$t = time$

$s = vt$

Graphs

Y-axis: $Distance$
X-axis: $Time$

For constant speeds the gradient of the straight line is equal to the speed.

Velocity

Speed in a given direction: Two objects moving in opposing directions at the same speed travel at the same $speed$, but not with the same $velocity$.

Acceleration

The change of velocity per unit of time. A negative value of $a$ is called $deceleration$.

Acceleration Unit

$m/s^2$

Constant Acceleration

$a = acceleration$
$s = \text{distance moved}$
$speeds = u, v$ (with speed changing from $u$ to $v$)

$a = \frac{v-u}{t}$

$average$ $speed = \frac 1 2 (u+v)$

$s = \frac 1 2 (u+v)t$

Graphs

Y-axis: $Speed$
X-axis: $Time$

Constant acceleration is the gradient of the line relative to the horizontal line at speed $u$.

The distance travelled given acceleration and time can be read from the area of the graph. It's equal to the area!

Distance

$1mile = 1.6kilometers$