Position, Velocity, and Acceleration

Position x

Displacement Initial Position x i Final Position x f Displacement

Average Velocity Starts here at a certain time Stops here at a certain time

Average Velocity Starts here at a certain time Stops here at a certain time More accurate the smaller the change is

Instantaneous Velocity Take the very small change in position over the very small change of time to be more accurate This will be equal to the slope of the position curve at a certain point Therefore is equal to the velocity at that point

Instantaneous Acceleration Same concept applies as velocity because acceleration is the change of velocity over time So the slope of the velocity equation give the acceleration at that point Therefore acceleration is equal to

Practice Problems The position of a particle is given by Since and And since and

Going backwards Sometimes an acceleration or velocity equation will be given instead In that case, you will have to reverse differentiate, or integrate Solve for C each time you integrate before integrating again, with the given information.

Practice problem

Guidelines A(t) is the slope of the v(t) equation Position is the integral of velocity, so is equal to the displacement from the starting point at t=x Someone always turns around when the velocity graph goes from the 4 th to 1 st or 1 st to 4 th quadrant.