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:
\(v=\frac{\Delta s}{\Delta t}\)
However, we can see that this definition corresponds to the slope of the curve in a position-time graph. In fact:
\(\Delta s\), the displacement, corresponds to the difference in position, so the difference between the values on the y-axis: \(\Delta s=y_2 -y_1\)
\(\Delta t\), the time interval, corresponds to the difference in times, so the difference between the values on the x-axis: \(\Delta t= t_2 -t_1=x_2 -x_1\)
So, the velocity is
\(v=\frac{\Delta s}{\Delta t}=\frac{y_2 -y_1}{x_2 -x_1}\)
which corresponds to the slope of the curve.
