6 The Relationship Between Acceleration Graphs slopeslopeareaareaderivativeCalculus:integral
7 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:
8 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.
9 Does a negative acceleration imply that an object is decreasing speed? What happens to velocity, ifa) the object starts from rest?Increases speed in the negative directionb) the object starts with a velocity of +15 m/s?first the object slows, momentarily stops, and then increases speed in the negative direction.
10 Negative Acceleration/Deceleration Misconception A negative acceleration does not imply deceleration (slowing). Deceleration only occurs when the velocity and acceleration are in opposite directions.
11 Acceleration Conventions VelocityDirectionAcceleration DirectionInitial ResultsLong Term Results+Speed IncreaseSpeed increase in positive direction-Speed DecreaseSlows to a momentary stop, then speed increase in negative directionSlows to a momentary stop, then speed increase in positive directionSpeed increaseSpeed increase in the negative direction
12 Acceleration: The slope of a velocity-time graph Proof:a = average accelerationThe slope a tangent of velocity-time graph gives theinstantaneous acceleration at a specific time.
14 Constant (Uniform) Acceleration vs Average Acceleration The average acceleration is equalto the instantaneous accelerationat all times between t1 and t2.The average acceleration factors the startingand ending velocities and time changes, butnot any velocity changes in between..Why?
15 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)v2+1046-30-20564t (s)2-15