Question

use this graph below for this question.
position of a runner moving in a straight line
graph
when is the runner moving at the fastest speed?
(a) between 0-70 seconds
(b) ...

Explanation:

To determine when the runner is moving at the fastest speed, we analyze the position - time graph. In a position - time graph, the speed of an object is given by the slope of the graph. The steeper the slope, the greater the speed.

Step 1: Analyze the slope in different intervals

• For the interval between 0 - 70 seconds: The graph is a line with a certain slope. Let's assume the change in position ($\Delta x_1$) and change in time ($\Delta t_1$) in this interval. The slope $m_1=\frac{\Delta x_1}{\Delta t_1}$.
• For the interval between 70 - 80 seconds: The graph is horizontal, which means the slope $m_2 = 0$ (the runner is at rest).
• For the interval between 80 - 110 seconds: The graph is a line with a slope. Let the change in position be $\Delta x_3$ and change in time be $\Delta t_3$. The slope $m_3=\frac{\Delta x_3}{\Delta t_3}$.

By visually inspecting the graph, we can see that the slope of the graph in the interval between 80 - 110 seconds is steeper than the slope in the interval between 0 - 70 seconds. A steeper slope implies a greater speed.

Since the problem seems to have some options (even though some are not fully visible, from the context of position - time graph and speed calculation), the runner is moving at the fastest speed in the interval where the slope of the position - time graph is the steepest. If we assume the options are like between 0 - 70, 70 - 80, 80 - 110 etc., the interval with the steepest slope (fastest speed) is likely the one with the most negative (or steepest positive, but in this case, since it's coming back, negative slope magnitude) slope.

If we assume the options are:
A. Between 0 - 70 seconds
B. Between 70 - 80 seconds
C. Between 80 - 110 seconds

The answer is C. Between 80 - 110 seconds (assuming this is the interval with the steepest slope).

Answer:

To determine when the runner is moving at the fastest speed, we analyze the position - time graph. In a position - time graph, the speed of an object is given by the slope of the graph. The steeper the slope, the greater the speed.

Step 1: Analyze the slope in different intervals

• For the interval between 0 - 70 seconds: The graph is a line with a certain slope. Let's assume the change in position ($\Delta x_1$) and change in time ($\Delta t_1$) in this interval. The slope $m_1=\frac{\Delta x_1}{\Delta t_1}$.
• For the interval between 70 - 80 seconds: The graph is horizontal, which means the slope $m_2 = 0$ (the runner is at rest).
• For the interval between 80 - 110 seconds: The graph is a line with a slope. Let the change in position be $\Delta x_3$ and change in time be $\Delta t_3$. The slope $m_3=\frac{\Delta x_3}{\Delta t_3}$.

By visually inspecting the graph, we can see that the slope of the graph in the interval between 80 - 110 seconds is steeper than the slope in the interval between 0 - 70 seconds. A steeper slope implies a greater speed.

Since the problem seems to have some options (even though some are not fully visible, from the context of position - time graph and speed calculation), the runner is moving at the fastest speed in the interval where the slope of the position - time graph is the steepest. If we assume the options are like between 0 - 70, 70 - 80, 80 - 110 etc., the interval with the steepest slope (fastest speed) is likely the one with the most negative (or steepest positive, but in this case, since it's coming back, negative slope magnitude) slope.

If we assume the options are:
A. Between 0 - 70 seconds
B. Between 70 - 80 seconds
C. Between 80 - 110 seconds

The answer is C. Between 80 - 110 seconds (assuming this is the interval with the steepest slope).