Now we proceed to a slightly more complicated type of motion which will
leads us to defining instantaneous velocity and acceleration.
If we raise one end of the air-track we have an inclined track. This time
I will start the cart from rest at the same time as I activate
the photo-gates. Again I obtain four entries in my x versus t
table:
This time the curve is more complicated. What does it remind you of (parabola). Again if I had a more elaborate mechanism I could measure more points and convince you that what we have indeed is a parabola.
I can again calculate the average velocity from start to end and I get
The average velocity again corresponds to the slope of the line
connecting 
to 
. As opposed to the previous case
however we see that if were to pick different time intervals we get different
average velocities. We can illustrate this by filling in another
column in the table as before with average velocities in respective
time intervals.The average velocity is increasing with time. If we want to pin
down how the velocity evolves with time I have got to choose a very small
time interval.