Displacement and Constant Velocity ($s$ and $v$)

• Change the velocity to and hit the Play button.
• Observe the relationship between the sign of $v$ and the slope of the curve in the $s$ vs $t$ graph.

Displacement, Velocity, and Acceleration ($s, v, a$)

• Change the acceleration to $-5m/s^2$ and hit the Play button.
• Adjust the acceleration and see how it affects the curve.
• Press the reset button (the circular arrow) to restart with the new initial velocity.

Catching Up

• Blue circle has a head start but moves with constant velocity.
• Red circle start at the origin from rest but accelerates.
• Press the reset button (the circular arrow) to restart with the new initial velocity and head start.
• Can you predict when and where they will meet up?

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)?

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 (\(\Delta v\)).

Free Fall in 1D

After pressing the reset button, drag the arrow to change the velocity.
Drag the ball to inspect the trajectory.
Observe how the vertical and horizontal directions evolve indpendently of each other.

The Trajectory of Projectile Motion

• Two trajectories are shown when you adjust the initial speed or angle.
• Pause then adjust the initial angle to see which angle will give maximum range.
• Calculate and predict the range and positions of the ball at different times. Compare with the simulation.