Position vs. time graphs Review (x vs. t) Remember that for a position vs time graph that linear lines show that object is moving at a constant velocity. The slope of the line at any point shows the instantaneous velocity of the object.

Position vs. time graphs (x vs. t) But what about curved lines like the one below?

Position vs. time graphs (x vs. t) A parabolic curve means that the slope (velocity) is not constant, so the object is accelerating. The object is either speeding up or slowing down.

Definition of Acceleration An acceleration is the change in velocity per unit of time. (A vector quantity.) Remember vector quantities have direction so acceleration can be + or -.

Average a Dv Dt v2 v1 t2 t1

Velocity vs. time graphs (v vs. t) Shows the change in velocity for an object over a period of time. The slope of the line at any point shows the instantaneous acceleration of the object.

Speed Up or Slow Down? If the velocity and acceleration both positive, the object speeds up. If the velocity and acceleration is both negative, the object speed up. If velocity and acceleration are opposite signs, the object slows down. Sames help each other (speed up) Opposites hurt each other (slow down).

Back to (x vs. t) graphs Positive accelerations cause concave up graphs. Negative accelerations cause concave down graphs.

CONCLUSION OF Velocity Time Graphs