does the slope of a distance vs. time graph show
the average velocity
or the
instaneous velocity
I'm asked the question and don't know which one. I believe that it would be the instaneous value because the slope is refering to one point on the graph... not sure though
You are right. Slope is measured tangent to the position-time curve. If the velocity is changing, there is only one tangent point. Slope of the tangent line is the instantaneous velocity
what if the velocity is kept constant
or is suppose to at least
If the velocity is constant (over a finite time interval) the average velocity during that interval and the instaneous velocity are the same.
Thanks =]
The slope of a distance vs. time graph represents the rate at which the distance is changing with respect to time. It can be used to determine both the average velocity and the instantaneous velocity, depending on the specific circumstances.
To understand this better, let's break it down:
1. Average Velocity: The average velocity is calculated by dividing the total distance covered by an object by the total time taken. It provides an overall measure of how fast an object is moving over a given time interval. To find the average velocity using a distance vs. time graph, you would draw a straight line connecting the initial and final points on the graph and determine the slope of that line. The slope of this line represents the average velocity.
2. Instantaneous Velocity: Unlike average velocity, which describes the overall rate of change over a specific time interval, instantaneous velocity refers to the velocity of an object at an exact moment in time. Since velocity is the rate of change of distance with respect to time, the instantaneous velocity can be determined by finding the slope of the tangent line to the distance vs. time graph at a specific point. This tangent line represents the instantaneous velocity at that moment.
Therefore, to answer your question, the slope of a distance vs. time graph can refer to both the average velocity (when connecting the initial and final points) and the instantaneous velocity (by finding the slope of the tangent line at a specific point).