Drag the Truck JavaScript Simulation Applet HTML5

Drag the Truck JavaScript Simulation Applet HTML5

Drag the Truck JavaScript Simulation Applet HTML5 (direct link) https://iwant2study.org/ospsg/index.php/611

This is a model of basic Newtonian kinematics, visualized via a truck simulation.

How to play:
1) Click the Play button to begin the simulation.
2) Drag the truck to plot the graph of the truck's movement with the red dotted line.
3) Try to get the red dotted line to match up with the blue one (representing the simulated path of the truck).

Try it for not just position, but velocity and acceleration graphs as well!Use the mouse to drag the front bumper of the toy truck (the red square). The goal of this exercise is to match the position/velocity/acceleration vs. time graphs as shown in the animation (position is given in centimeters and time is given in seconds). There is some smoothing for the velocity and acceleration matching animations.

Answer the following questions after trying to match the motion:

1. Which of the graphs was the easiest to match and which one was the hardest to match? 
1. position
2. Why? Base your answer on physics and mathematics.
1. the position is easiest to match due to the direct match of the position of drag square to the position of the line graph. More difficult to match motion is the velocity which is the rate of change of position with respect to time, $ v = \frac{dx}{dt} = \frac{x_{2}-x_{1}}{t_{2}- t_{1}}$. Thus, a small change in dx will result in a big change in velocity. The acceleration is the hardest for the same reason, a small change in dv will result in an extremely large change in acceleration a.   $ a = \frac{dv}{dt} = \frac{v_{2}-v_{1}}{t_{2}- t_{1}}$