Acceleration. Velocity and Acceleration Formal definitions.

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Presentation transcript:

Acceleration

Velocity and Acceleration Formal definitions

Velocity and Acceleration Formal definitions

Exercise The motion of a particle in the x-direction is given by: a)Find the velocity function, v(t) b)Find the acceleration function, a(t) c)When (if ever) is the velocity v=0? What is the acceleration and position at that time?

Exercise Draw x(t), v(t) and a(t) diagrams to describe the motion. Stack the graphs vertically so that a vertical line connects equal values of t on each of the three graphs. V 0 >0

Constant acceleration A useful special case of motion is that of constant acceleration, where a(t)=a avg =a for all times t. a)Write an equation to describe the velocity v(t) at any time t. What does this look like graphically? b)Write an equation to describe the position x(t) at any time t. What does this look like graphically?

Constant acceleration Objects in gravitational free-fall experience constant acceleration. The acceleration depends on the location on Earth, and height above the surface, but we will approximate: This is independent of the mass of the falling body! We will revisit this amazing fact later.

Sample Problems Sample 2-7: A pitcher tosses a baseball up along a y axis, with an initial speed of 12 m/s. a)How long does the ball take to reach its maximum height? b)What is the ball’s maximum height above its release point? c)How long does the ball take to reach a point 5.0 m above its release point?

Applets Analyzing Motion Using Diagrams 1.2 Analyzing Motion Using Graphs 1.3 Predicting Motion from Graphs 1.4 Predicting Motion from Equations 1.7 Problem