Question

position vs time for three runners which runner had the fastest speed in the race? which runner had the slowest speed in the race? which runner had a head start?

Explanation:

To solve questions about the position - time graph of the three runners, we use the concepts related to the slope of the position - time graph (which represents speed) and the initial position (which indicates a head start).

1. Fastest Speed

In a position - time graph, the speed of an object is given by the slope of the graph, where \(v=\frac{\Delta x}{\Delta t}\) (change in position over change in time). A steeper slope means a larger value of \(\frac{\Delta x}{\Delta t}\), and thus a greater speed. By looking at the graph, we can see that Runner A has the steepest slope among the three runners. So, Runner A has the fastest speed.

2. Slowest Speed

Again, using the concept of the slope of the position - time graph (\(v = \frac{\Delta x}{\Delta t}\)), a less - steep slope means a smaller value of \(\frac{\Delta x}{\Delta t}\), and thus a lower speed. Among the three runners, Runner C has the least - steep slope. So, Runner C has the slowest speed.

3. Head Start

A head start means that at \(t = 0\) (the start of the time measurement), the runner has a non - zero position. Looking at the graph, at \(t=0\) (the y - intercept of the graph), Runner C has a position greater than 0, while Runners A and B start from \(x = 0\) at \(t = 0\). So, Runner C had a head start.

Answer:

s:

• Which runner had the fastest speed in the race? Runner A
• Which runner had the slowest speed in the race? Runner C
• Which runner had a head start? Runner C