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zoom zoom Acceleration

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Acceleration Terms Acceleration (a)– the rate of change of velocity (can be +, -, or centripetal) Deceleration– only negative acceleration (slowing down) Centripetal Acceleration– acceleration that occurs when changing direction (turning) Freefall– objects falling due to gravity Force is what you feel when you accelerate

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3 ways to accelerate Since acceleration is a change in velocity and velocity has 2 parts We can accelerate by Changes in speed Speed up (+ acceleration) Slow down (- acceleration) Changing Direction Turning Changing both speed and direction

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**Your speedometer – the key to accel**

We don’t see acceleration of an object well with our eyes But if we look at a speedometer we can see speed change. Acceleration is a picture of what your speedometer is doing

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**Acceleration is a pic of your Speedo**

Slow Acceleration Fast(er) Acceleration Acceleration is a pic of your Speedo

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**The Acceleration Graph Setup**

The Variables The Graph Speed ( or velocity)is the dependent variable Time is the independent variable Graph setup = Formula Speed Dsp a= Dt Time The Acceleration Graph Setup

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**Acceleration& Slope (quick version)**

Acceleration(Dsp/Dt)= slope on an acceleration graph (rise/run) Acceleration Graph + acceleration (gas pedal) Constant Speed (0 acceleration) (cruise control) Speed Acceleration (deceleration) (brake pedal) No motion - stopped Time

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**Acceleration Graphs & Slope & speed**

Positive (+) slope = + accel (speeding up) t speed Negative (-) slope = - accel (slowing down) t speed Zero (0) slope (flat line) = 0 accel (constant speed)

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**Slope & Type of Acceleration**

Steeper slopes show greater acceleration Straight lines = Constant acceleration Steady increase or decrease in speed Accelerates quickly speed t speed t decelerates slowly Accelerates slowly decelerates quickly When is the speed = to 0 (stopped)?

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Discuss This graph Describe which sport you think this graph represents and why. Golf Skydiving Fishing 100-meter dash Drag racing Speed Time

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**Calculating Acceleration from Slope**

Rise–change in the graph on the vertical axis (Speed) Run–change in the graph on the horizontal axis (Time) Slope = = Y2-y1 X2-x1 rise run Acceleration= sp2-sp1 t2-t1 P1 (0 s, 0 km/h) t1 sp1 P2 (20 s, 20 km/h) t sp2 P2 a= sp2-sp1 t2-t1 = 20 km/h - 0 km/h 20 s– 0 s 20 km/h 20 s = P1 = 1 km/h/s

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**Answers to Sample Questions**

What is the acceleration of the object from 0 – 20 s? What is the speed of the object from 20 – 40 s? What is the speed of the object from 40 – 60 s? sp2 – sp 1 (rise) (20–0 m/s) 20 m/s Acceleration(slope) = = = = 1 m/s/s t2 – t (run) ( 20 – 0 s) 20 s sp2 – sp 1 (rise) (20–20 m/s) 0 m/s Acceleration(slope) = = = = 0 m/s/s t2 – t (run) ( 40 – 20 s) 20 s sp2 – sp 1 (rise) (0–20 m/s) -20 m/s Acceleration(slope) = = = = -1 m/s/s t2 – t (run) ( 60 – 40 s) 20 s

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**Acceleration Formula, Units & Power Shape**

m/s, cm/min, km/h Acceleration = final speed – initial speed final time – intial time m/s/s, cm/min/min, km/h/s s, min, hr Since: sp2 = final speed, sp1 = initial speed t2 = final time, t1 = initial time a = (spf – spi) (tf – ti) a = (sp2 – sp1) (t2 – t1)

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**Acceleration Formula, Units & Power Shape**

= final speed – start speed final time – start time sp2=final speed, sp1=start speed t2=final time, t1=start time Since: Then: ÷ Dsp a = D sp D t Dsp = sp2 – sp1 a Dt Dt = t2 – t1 or x

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**Using the Acceleration Power Shape**

or x a Dt Dsp ÷ A kid is sledding down a hill. When he enters the course his speed is 10 m/s. After 2 seconds he has reached a speed of 26 m/s. What was his acceleration? Given Formula Setup Solution List Given Info And Unknown: sp1 = 10 m/s sp2 = 26 m/s Dt = 2 s a= ? Show Needed Equations: a = Substitute with Units & Show Math: a = Circles Answer with Units: a = a = 8 m/s/s (sp2 – sp1) 26 m/s-10 m/s 16 m/s Dt 2 s 2 s

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**Freefall and gravitational acceleration**

Freefall: Objects falling due to gravity All objects accelerate at the same rate due to gravity during freefall regardless of their mass Objects may reach terminal velocity sooner due to air resistance Gravitational acceleration (g) = 9.8 m/s/s on earth

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**Using the Acceleration Power Shape**

or x a Dt Dsp ÷ A woman jumps from a plane. She opens her parachute five seconds later. How fast was she going when she opened her shoot (disregard air resistance)? Given Formula Setup Solution List Given Info And Unknown: Dsp = ?? Dt = 5 s a= g=9.8 m/s/s Show Needed Equations: Dsp = Substitute with Units & Show Math: Dsp = Circles Answer with Units: Dsp = 49.2 m/s a · Dt 9.8 m/s/s · 5 s

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