Speed and average speed

1. Speed is a scalar quantity because it has magnitude but no direction.
2. The equation for average speed is
3. $$average\; speed=\frac{distance\; travelled}{time\; taken}$$
4. Using symbols,
5. $$v=\frac{s}{t}$$
6. where $v$ is average speed in $m/s$, $s$ is distance in $m$ and $t$ is time in $s$.
7. The rearranged forms are $s=vt$ and $t=\frac{s}{v}$. Convert every measurement to compatible units before substitution.

Average speed for a whole journey

1. Average speed is not normally the arithmetic mean of two speeds. It depends on the total distance and total time.
2. Include time spent stationary because it contributes to the total journey time even though no distance is travelled during that interval.

Distance–time graphs

1. A distance–time graph shows distance on the vertical axis and time on the horizontal axis.
2. The gradient represents speed because
3. $$gradient=\frac{\Delta distance}{\Delta time}=speed$$
4. A horizontal line has zero gradient, so the object is stationary.
5. A straight sloping line has constant gradient, so the object moves at constant speed.
6. A steeper line represents a greater speed because more distance is covered in the same time.
7. A curve with an increasing gradient represents increasing speed. A curve that becomes less steep represents decreasing speed.

Calculating a graph gradient

1. Choose two points far apart on the straight section of the graph. If a best-fit line is present, the points should lie on that line and do not need to be plotted data points.
2. Draw a large gradient triangle and read the coordinate differences from the axes.
3. Calculate
4. $$speed=\frac{d_2-d_1}{t_2-t_1}$$
5. Include the unit obtained from the graph axes, commonly $m/s$.