Putting it All Together

Consider the case of constant acceleration. An object is held at a cliff edge and dropped. We know the acceleration, and we know that acceleration is the derivative of velocity. We can integrate the acceleration to get the velocity, and integrate the velocity to get the trajectory (position) of the object after it has been dropped.

1. plot the acceleration as a graph versus time, and calculate the change in velocity as the area under the curve over the time elapsed.
   • Delta V = A*T
   • V new = V old + Delta V
   • V(t) = Vzero + At
2. calculate the anti-derivative of a constant function, since the curve which has the same slope everywhere is just a line, this is
   • v=vzero +At where A is the slope of the line, and the intercept is take from the initial value of v.
3. calculate the accumulated change over small intervals.
   • assume some initial condition
   • calculate a change at the current rate of change
   • determine if the function being integrated has changed (for this problem, since it is a constant, it does not)
   • reevaluate until the desired time has been reached.

Quick Quiz: Which of the following sets of graphs match?
acceleration = , velocity = ,
position =
acceleration = , velocity = ,
position =
acceleration = , velocity = ,
position =
acceleration = , velocity = ,
position =