Question

The ____ of a position-time graph represents an object’s velocity.

Answer 1

The slope of a position-time graph represents an object’s speed.

You can't determine the object's velocity from the graph, because
the graph only tells you the distance the object moves, but not the
direction.

Answer 2

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.