Acceleration Chapter 2 Section 2

Acceleration Acceleration – The quantity that describes the rate of change of velocity in a given time interval. Average Acceleration – The average change in velocity divided by the change in time.

Acceleration Equation 𝑎 𝑎𝑣𝑔 = ∆𝑣 ∆𝑡 = 𝑣 𝑓 − 𝑣 𝑖 𝑡 𝑓 − 𝑡 𝑖 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛= 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑣𝑒𝑙𝑐𝑖𝑡𝑦 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡𝑖𝑚𝑒

Acceleration Units The SI units for acceleration “m/s²” Acceleration = velocity/time = m/s/s = m/s²

Acceleration Vector Acceleration is a vector quantity Has both magnitude and direction Since acceleration is a vector, it can have a positive or negative value. If acceleration and velocity are in the same direction, the object speeds up. If the acceleration and velocity are in opposite directions, the object slows downs.

Acceleration Chart Vi a Motion + - + or - Speeding up Slowing down Constant velocity Speeding up from rest Remains at rest

Graphing Linear Motion The slope and shape of a single graph can describe the motion of an object’s displacement, velocity, and acceleration vs. time. Slope = rise / run Rise – Dependant Variable (y-axis) Run – Independent Variable (x-axis)

Relating Displacement, Velocity and Acceleration On a Displacement vs. Time graph Rise / Run = Slope Displacement / Time = Velocity The tangent line of a single point on a (d vs. t) graph is equal to the instantaneous velocity at that moment in time. On a Velocity vs. Time graph Velocity / Time = Acceleration The tangent line of a single point on a (v vs. t) graph is equal to the instantaneous acceleration at that moment in time.

Graphing Hints d vs. t V vs. t a vs. t => => => Slope Area Slope = Velocity V vs. t Slope = Acceleration a vs. t Area = Velocity V vs. t Area = Displacement => => =>

Graph of a Single Object In Motion displacement vs. time velocity vs. time acceleration vs. time d v a t t t

Object In Free Fall displacement vs. time velocity vs. time acceleration vs. time d v a t t t