1. Acceleration

2. Changing Velocity  In complicated motion the velocity is not constant.  We can express a time rate of change for velocity just as for position,  v = v 2 - v 1.  The average acceleration is the time rate of change of velocity: a =  v /  t.

3. Average Acceleration Example problem  A jet plane has a takeoff speed of 250 km/h. If the plane starts from rest, and lifts off in 1.2 min what is the average acceleration? a =  v /  t = [(250 km/h) / (1.2 min)] * (60 min/h) a =  v /  t = [(250 km/h) / (1.2 min)] * (60 min/h) a = 1.25 x 10 4 km/h 2 a = 1.25 x 10 4 km/h 2  Why is this so large? Is it reasonable?  Does the jet accelerate for an hour?

4. Instantaneous Acceleration  Instantaneous velocity is defined by the slope.  Instantaneous acceleration is also defined by the slope. v t P1P1 P2P2 P3P3 P4P4

5. Velocity to Position  Area under a velocity curve equals the change in position. v t P1P1 P2P2 P3P3 P4P4

6. Acceleration to Velocity  Area under an acceleration curve equals the change in velocity.  Negative area is a decrease in value. a t P1P1 P2P2 P3P3 P4P4 v t P1P1 P2P2 P3P3 P4P4

7. Velocity in Two Dimensions  Position graph with velocity vectors.  Velocity graph using an origin with zero speed. y x vyvy vxvx

8. Acceleration in Two Dimensions  The acceleration shows the change in velocity.  Acceleration, velocity and position may not line up. y x vyvy vxvx

9. Vector Equations  Like velocity, acceleration equations can be written by components. next For constant acceleration: