Acceleration Changing Velocity In complicated motion the velocity

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 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/h 2 ] ] Why is this so large? Is it reasonable? Does the jet accelerate for an hour?

Instantaneous Acceleration ] Instantaneous velocity is defined by the slope. ] Instantaneous acceleration is also defined by the slope. v P 2 P 1 P 3 t P 4

Velocity to Position ] Area under a velocity curve equals the change in position. v P 2 P 1 P 3 t P 4

Acceleration to Velocity ] Area under an acceleration curve equals the change in velocity. ] Negative area is a decrease in value. v a P 2 P 1 P 2 t P 4 P 3 t P 4

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

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

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