The graph below represents the journey of a cyclist. (a) Name an instrument that could be used to measure the time taken for the journey. \( \qquad \) stopwatch (b) Calculate the average speed of the cyclist as he travelled from point \( \mathbf{A} \) to point \( \mathbf{B} \). Calculation

**(a)** A stopwatch **(b)** 1. Let the distance covered from point \( \mathbf{A} \) to point \( \mathbf{B} \) be \(\Delta d\) and the time taken be \(\Delta t\). 2. The average speed, \( v_{\text{avg}} \), is given by the formula \[ v_{\text{avg}}=\frac{\Delta d}{\Delta t}. \] 3. From the graph (using the appropriate scale) determine the distance at point \( \mathbf{A} \) and at point \( \mathbf{B} \). The difference is \[ \Delta d = \text{(distance at } \mathbf{B}\text{)} - \text{(distance at } \mathbf{A}\text{)}. \] 4. Similarly, determine the times at \( \mathbf{A} \) and \( \mathbf{B} \) so that \[ \Delta t = \text{(time at } \mathbf{B}\text{)} - \text{(time at } \mathbf{A}\text{)}. \] 5. Substitute these values into the formula above. For example, if the graph shows that the cyclist travelled \(30\) km in \(1.5\) hours then \[ v_{\text{avg}}=\frac{30\text{ km}}{1.5\text{ h}}=20\text{ km/h}. \] Thus, the average speed of the cyclist from point \( \mathbf{A} \) to point \( \mathbf{B} \) is calculated by dividing the distance traveled by the time taken.