What is the rate change in position called?

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Presentation transcript:

What is the rate change in position called? velocity

Acceleration Rate change in velocity magnitude and/or direction. Vector quantity. SI units are m/s2. Slope of a velocity-time graph.

Acceleration occurs with an increase or decrease in speed and/or change in direction.

Graphs of Acceleration

The Relationship Between Acceleration Graphs slope slope area area derivative Calculus: integral

Interpretation of Acceleration Graphs Only a parabola for a position-time graph implies constant (uniform) acceleration. Any other curve for a position-time or any curve for a velocity-time graph implies a non-uniform acceleration. Calculus explanation:

Acceleration Units Meaning What does an acceleration of +20 m/s2 mean? An increase of speed in the positive direction of 20m/s for each second.

Does a negative acceleration imply that an object is decreasing speed? What happens to velocity, if a) the object starts from rest? Increases speed in the negative direction b) the object starts with a velocity of +15 m/s? first the object slows, momentarily stops, and then increases speed in the negative direction.

Negative Acceleration/Deceleration Misconception A negative acceleration does not imply deceleration (slowing). Deceleration only occurs when the velocity and acceleration are in opposite directions.

Acceleration Conventions Velocity Direction Acceleration Direction Initial Results Long Term Results + Speed Increase Speed increase in positive direction - Speed Decrease Slows to a momentary stop, then speed increase in negative direction Slows to a momentary stop, then speed increase in positive direction Speed increase Speed increase in the negative direction

Acceleration: The slope of a velocity-time graph Proof: a = average acceleration The slope a tangent of velocity-time graph gives the instantaneous acceleration at a specific time.

Acceleration Equation a = average acceleration

Constant (Uniform) Acceleration vs Average Acceleration The average acceleration is equal to the instantaneous acceleration at all times between t1 and t2. The average acceleration factors the starting and ending velocities and time changes, but not any velocity changes in between.. Why?

Area of an Acceleration-Time Graph The area of an acceleration-time graph yields the change in velocity for that interval. a (m/s2) t (s) ∆v (m/s) v 2 +10 4 6 -30 -20 5 6 4 t (s) 2 -15