Constant_Acceleration-VPython.ipynb

Kernel: Python 2 (SageMath)

For an object that is accelerating, you need to update the velocity at each time step in addition to updating the position. The easiest way to update velocity is to use the definition of acceleration:

$$\vec{a}=\frac{\vec{v}_f - \vec{v}_i}{t_f - t_i}$$$$\vec{v}_f = \vec{v}_i + \vec{a}(t_f - t_i)$$

Because of the way compute programs work, the line ball.vel = ball.vel + g*dt is equivalent to the above equation. In other words, Python calculates everything to the right of the equals sign and then assigns it to the variable to the left. This means that ball.vel on the right side is the initial velocity $\vec{v}_i$, while ball.vel on the left side is actually the final velocity $\vec{v}_f$.

Run the code below to see a ball moving with a constant gravitational force.

from vpython import *

scene=canvas()  #Create canvas to draw on
graph_screen=graph(width=400,height=400,xtitle='time', ytitle='Position',xmin=0,xmax=3,ymin=-10,ymax=10)
pos_graph = gcurve(color=color.blue, width=4)   #Create curve to plot position vs. time
graph_screen2=graph(width=400,height=400,xtitle='time', ytitle='Velocity', xmin=0,xmax=3,ymin=-20,ymax=10)
vel_graph = gcurve(color=color.red,width=3)   #Curve for velocity



ground=box(pos=vector(0,-1,0),axis=vector(1,0,0),length=20,height=0.1,color=color.green)  #Grass-colored box for reference

ball=sphere(color=color.blue)   #Create the ball
ball.vel=vector(10,10,0)  #Give ball a velocity
attach_arrow(ball,"vel",scale=.5,color=color.yellow)  #Attach an arrow to show velocity
attach_trail(ball,color=color.yellow,type="points",retain=10,pps=1)

g=vector(0,-9.8,0)  
dt=0.01
t=0

while t<300:
    rate(30)
    ball.pos=ball.pos+ball.vel*dt   #update position
    ball.vel=ball.vel + g*dt  #update velocity
    position=ball.pos.y   #For plotting position
    velocity=ball.vel.y   #For plotting velocity
    time=t*dt     #For plotting
    pos_graph.plot(pos=(time,position))   #Plot a single data point on the graph
    vel_graph.plot(pos=(time,velocity))
    t=t+1   #Advance time step

<IPython.core.display.Javascript object>

For You To Try

• Add a second object with a different initial velocity

• Add curves to both graphs for this new object and plot the y-position and y-velocity