Answer:
The slope of a position-time graph represents an object’s velocity.
Explanation:
In a position-time graph, the values on the x-axis represent the time, while the values on the y-axis represent the position of the object.
Velocity is defined as the ratio between the displacement of an object and the time taken:
[tex]v=\frac{\Delta s}{\Delta t}[/tex]
However, we can see that this definition corresponds to the slope of the curve in a position-time graph. In fact:
[tex]\Delta s[/tex], the displacement, corresponds to the difference in position, so the difference between the values on the y-axis: [tex]\Delta s=y_2 -y_1[/tex]
[tex]\Delta t[/tex], the time interval, corresponds to the difference in times, so the difference between the values on the x-axis: [tex]\Delta t= t_2 -t_1=x_2 -x_1[/tex]
So, the velocity is
[tex]v=\frac{\Delta s}{\Delta t}=\frac{y_2 -y_1}{x_2 -x_1}[/tex]
which corresponds to the slope of the curve.
