Copyright © 2010 Pearson Education, Inc. Chapter 3 Acceleration & Accelerated Motion

Copyright © 2010 Pearson Education, Inc. 3.1 Acceleration Average acceleration: the rate at which velocity changes with time. acceleration has direction (vector quantity) The dimensions of average acceleration are the dimensions of velocity per time or (meters per second) per second.

Copyright © 2010 Pearson Education, Inc. 3.1 Acceleration Acceleration occurs when there is a: 1.change in speed. 2.change in direction. (ie: turning) 3.change in speed and direction.

Copyright © 2010 Pearson Education, Inc. 3.1 Acceleration Speed increases when the velocity and acceleration have the same signs (direction).  A car moving in the positive direction  A car moving in the negative direction

Copyright © 2010 Pearson Education, Inc. 3.1 Acceleration Speed decreases when the velocity and acceleration have opposite signs (direction). “deceleration”  A car moving in the positive direction with negative acceleration.  A car moving in the negative direction with positive acceleration.

Copyright © 2010 Pearson Education, Inc. 3.1 Acceleration Acceleration can be determined graphically by the slope on a v vs. t graph.

Copyright © 2010 Pearson Education, Inc. 3.1 Acceleration

Copyright © 2010 Pearson Education, Inc. 3.2 Motion with Constant Acceleration The distance traveled by an object is equal to the area under its velocity-time graph.

Copyright © 2010 Pearson Education, Inc. 3.2 Motion with Constant Acceleration If the acceleration is constant:

Copyright © 2010 Pearson Education, Inc. 3.2 Examples A driver traveling at 15.0 m/s east sees Miley Cyrus standing in the middle of the road twerking. He begins to accelerates at 3.0 m/s 2 in an attempt to run her over. If he accelerates for 18.0 s, how fast is he going when he crashes into her?

Copyright © 2010 Pearson Education, Inc. 3.2 Examples A drag racer starts from rest and accelerates at 7.0 m/s 2. How far will it travel in (a) 1.00 s, (b) 2.00 s, (c) 3.00 s?

Copyright © 2010 Pearson Education, Inc. 3.2 Examples A ranger, driving at 11.4 m/s, sees a deer 20.0 m ahead and applies the brakes. If he decelerates at 3.80 m/s 2, how much distance is required for the car to come to rest?

Copyright © 2010 Pearson Education, Inc. 3.3 Position-Time for Constant Acceleration For constant acceleration the relationship between position and time is not linear! Constant acceleration produces a parabolic position-time graph.

Copyright © 2010 Pearson Education, Inc. 3.3 Position-Time for Constant Acceleration If the graph curves up, then the acceleration is positive. If the graph curves down, then the acceleration is negative.

Copyright © 2010 Pearson Education, Inc. Position-Time Graphs for Constant Acceleration In general, the greater the curvature of the parabola, the greater the magnitude of the acceleration.

Copyright © 2010 Pearson Education, Inc. 3.3 Position-Time for Constant Acceleration

Copyright © 2010 Pearson Education, Inc. 3.4 Freely Falling Objects Free fall is the motion of an object subject only to the influence of gravity. The acceleration due to gravity is a constant, g.

Copyright © 2010 Pearson Education, Inc. 3.4 Freely Falling Objects An object falling in air is subject to air resistance (and therefore is not freely falling).

Copyright © 2010 Pearson Education, Inc. 3.4 Freely Falling Objects Free fall from rest: Velocity increases linearly with time. Distance increase with time squared!

Copyright © 2010 Pearson Education, Inc. 3.4 Freely Falling Objects The motion of objects in free fall is symmetrical. A position-time graph of free-fall motion reveals this symmetry.