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Acceleration

Acceleration. 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. Average Acceleration.

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Acceleration

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  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 = v2 - v1. • The averageacceleration 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 = 1.25 x 104 km/h2 • Why is this so large? Is it reasonable? • Does the jet accelerate for an hour?

  4. Instantaneous velocity is defined by the slope. Instantaneous acceleration is also defined by the slope. v P2 P1 P3 t P4 Instantaneous Acceleration

  5. Area under a velocity curve equals the change in position. v P2 P1 P3 t P4 Velocity to Position

  6. Area under an acceleration curve equals the change in velocity. Negative area is a decrease in value. a v P1 P2 P1 P2 t P3 t P4 P3 P4 Acceleration to Velocity

  7. Position graph with velocity vectors. Velocity graph using an origin with zero speed. Velocity in Two Dimensions y vy x vx

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

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

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