Question

the graph shows the position of four runners over a 5 - minute interval. order the runners from fastest to slowest.
runner position
position (m)
time (min.)
runner 1
runner 2
runner 3
runner 4
runner 1
runner 2
runner 3
runner 4

Explanation:

Step1: Understand the relationship between speed and the graph

In a position - time graph, speed \(v=\frac{\Delta x}{\Delta t}\), where \(\Delta x\) is the change in position and \(\Delta t\) is the change in time. The steeper the line (larger the slope), the higher the speed.

Step2: Analyze the slopes of the lines for each runner

• For runner 3: The line is the steepest. If we consider the time interval \(t = 5\) minutes (\(\Delta t=5\) min), and assume the final position \(x_3\approx1400\) m (initial position \(x_{0}=0\) m). The slope \(m_3=\frac{1400 - 0}{5}=280\) m/min.
• For runner 1: If the final position \(x_1\approx1100\) m (initial position \(x_{0}=0\) m), the slope \(m_1=\frac{1100 - 0}{5} = 220\) m/min.
• For runner 4: If the final position \(x_4\approx700\) m (initial position \(x_{0}=0\) m), the slope \(m_4=\frac{700 - 0}{5}=140\) m/min.
• For runner 2: If the final position \(x_2\approx600\) m (initial position \(x_{0}=0\) m), the slope \(m_2=\frac{600 - 0}{5}=120\) m/min.

Answer:

Runner 3, Runner 1, Runner 4, Runner 2