What slope would a person have on a distance-time graph if they were speeding, slowing down, or not moving at all?
On a distance-time graph, the slope of a line represents the speed or velocity of an object. Here's how to determine the slope and interpret it in the context of speeding, slowing down, or not moving at all:
1. Speeding up: If an object is speeding up, the slope of the distance-time graph will be positive and increasing. This means that the object is covering a greater distance in the same amount of time, indicating an increase in speed.
To calculate the slope, choose two points on the graph that represent different times and distances. Then, divide the change in distance by the change in time: slope = (change in distance) / (change in time).
2. Slowing down: When an object is slowing down, the slope of the distance-time graph will be positive but decreasing. This implies that the object is covering a smaller distance in the same amount of time, signifying a decrease in speed.
Similar to calculating the speed, select two points on the graph at different times and distances. Divide the change in distance by the change in time to find the slope.
3. Not moving at all: If an object is not moving or at rest, the distance-time graph will be a horizontal line with a slope of zero. This is because there is no change in distance over a given amount of time.
To confirm this, choose any two points on the graph that have the same time. The change in distance between these points will be zero, therefore making the slope zero as well.
By analyzing the slope on a distance-time graph, you can determine whether a person or object is speeding up, slowing down, or not moving at all.