Drag the mouse across the graph to see how the slope of the top graph determines the value of the graph at the bottom.

There are 10 examples altogether, press "Next Example" to see.

Rule 1: Slope of a displacement-vs-time (\(st\)) graph gives the velocity (\(v\)).

Rule 2: Slope of a velocity-vs-time (\(vt\)) graph gives the acceleration (\(a\)).#### Activity

Which examples represent the motion (displacement, velocity, and acceleration) of an object flying vertically under the influence of gravity (free fall)?

There are 10 examples altogether, press "Next Example" to see.

Rule 1: Slope of a displacement-vs-time (\(st\)) graph gives the velocity (\(v\)).

Rule 2: Slope of a velocity-vs-time (\(vt\)) graph gives the acceleration (\(a\)).

Drag the mouse across the graph to see how the area of the top graph determines the value of the graph at the bottom.

For simplicity, we will assume the initial value of \(s\) or \(v\) at the bottom graph to be zero, so \(\Delta s = s\) and \(\Delta v = v\).

There are 6 examples altogether, press "Next Example" to see.

Rule 1: Area of a velocity-vs-time (\(vt\)) graph gives the change in displacement (\(\Delta s\)).

Rule 2: Area of a acceleration-vs-time (\(at\)) graph gives the velocity (\(\Delta v\)).

For simplicity, we will assume the initial value of \(s\) or \(v\) at the bottom graph to be zero, so \(\Delta s = s\) and \(\Delta v = v\).

There are 6 examples altogether, press "Next Example" to see.

Rule 1: Area of a velocity-vs-time (\(vt\)) graph gives the change in displacement (\(\Delta s\)).

Rule 2: Area of a acceleration-vs-time (\(at\)) graph gives the velocity (\(\Delta v\)).

After pressing the reset button, drag the arrow to change the velocity.

Drag the ball to inspect the trajectory.

Observe how the vertical and horizonatal directions evolve indpendently of each other.

Drag the ball to inspect the trajectory.

Observe how the vertical and horizonatal directions evolve indpendently of each other.