On a plot of position x versus time t for an object’s motion, what corresponds to the object’s average velocity between instant t1 and instant t2?
(a) intercept of the plot on the horizontal axis
(b) intercept of the plot on the vertical axis
(c) slope of a line connecting the corresponding points on the plot
(d) inverse of the slope of a line connecting the corresponding points on the plot
To find the object's average velocity between two instants of time on a position versus time graph, you need to calculate the slope of the line connecting the corresponding points on the plot.
So, the correct answer is (c) - the slope of a line connecting the corresponding points on the plot.
Here's how you can explain it:
Start by identifying the position x values at time t1 and t2 on the graph. These will be the coordinates (x1, t1) and (x2, t2), respectively.
Next, calculate the change in position (Δx) by subtracting the initial position from the final position, Δx = x2 - x1.
Then, calculate the change in time (Δt) by subtracting the initial time from the final time, Δt = t2 - t1.
Finally, divide the change in position (Δx) by the change in time (Δt) to get the average velocity (v) between t1 and t2: v = Δx / Δt.
By calculating the slope of the line connecting (x1, t1) and (x2, t2), you are essentially finding the average velocity of the object during that time interval.