Question

Time-displacement plots of walking stages. (The plot for the walking stage assumes a constant rate of walking.) The slope of the straight line joining the origin and the point labelled "Station" is the average velocity for the trip, from the beginning to the station.

Answer 1

The average velocity for the trip, from the beginning to the station, is given by the slope of the straight line connecting the origin and the point labeled "Station" on the time-displacement plot.

Step-by-step explanation:

In physics, average velocity is defined as the change in displacement
`(\(Δx\))` divided by the change in time
`(\(Δt\))`. When represented graphically on a time-displacement plot, the slope of the straight line connecting two points indicates the average velocity between those points. In this scenario, the point labeled "Station" represents the final position after the walking stage. By drawing a straight line from the origin to this point, we effectively create a right-angled triangle. The slope of this line
`(\(Δx/Δt\))` is the average velocity for the entire walking stage.

To calculate the average velocity, we use the formula:
`\[ \text{Average Velocity} = \frac{\text{Change in Displacement}}{\text{Change in Time}} \]` In the context of the time-displacement plot, the change in displacement
`(\(Δx\))` is the vertical distance from the origin to the "Station" point, and the change in time
`(\(Δt\))` is the horizontal distance. Therefore, the slope of the line provides the average velocity for the walking stage from the beginning to the station.

In summary, the average velocity for the trip is determined by the slope of the straight line connecting the origin and the point labeled "Station" on the time-displacement plot. This graphical representation allows for a visual interpretation of the average velocity in the context of the walking stages.