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Acceleration and Free Fall Chapter 2.2 and 2.3

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What is acceleration? Acceleration measures the rate of change in velocity. Average acceleration = change in velocity/ time required for change

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Units for acceleration

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Sign is very important! Acceleration has both direction and magnitude A negative value for acceleration does not always mean an object is decelerating!!

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Speeding up, moving to the left Slowing down, moving to the rightSpeeding up, moving to the right 2-4 Acceleration Increasing speed and deceleration (decreasing speed) should not be confused with the directions of velocity and acceleration: Slowing down, moving to the left

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Fill in the Chart Initial VelocityAccelerationMotion ++ Speeding up, moving right/up -- Speeding up, moving left/down +- Slowing Down moving right/up -+ Slowing Down, moving left/down - or +0 Constant Velocity 0- or + Speeding up from rest 00 Remaining at rest

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Graph of Velocity vs Time Question: What does the slope of this graph give you? Rise = Δv Run Δt Answer: ACCELERATION V f – V AVG = Δv t f – t i = Δt

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The Kinematic Equations You are going to loooooove these!

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Motion with constant acceleration Kinematic Equations The relationships between displacement, velocity and constant acceleration are expressed by equations that apply to any object moving with constant acceleration.

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Displacement with constant acceleration Δx = displacement V i = initial velocity V f = final velocity Δt = time interval

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Example: #1 p.53 in book A car accelerates uniformly from rest to a speed of 23.7 km/h in 6.5 s. Find the distance the car travels during this time. Δx = displacement= distance= ? V i = initial velocity = rest = 0 km/h V f = final velocity = 23.7 km/h Δt = time interval = 6.5 s Look at final velocity…convert to m/s!!!

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Problem Solving Final velocity conversion Plug in values and solve for Δx

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Velocity with constant uniform acceleration V f = final velocity V i = initial velocity a = acceleration Δt = time interval

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Example: #2 p.55 An automobile with an initial speed of 4.30 m/s accelerates uniformly at the rate of 3.0 m/s 2. Find the final speed after 5.0 seconds. V f = final velocity=? V i = initial velocity = 4.3 m/s a = acceleration= 3.0 m/s^2 Δt = time interval= 5.0 s

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Solve Plug in values and solve for Vf V f = 19 m/s

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Displacement with constant uniform acceleration Δx = displacement V i = initial velocity a = acceleration Δt = time interval

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Example: #2 p.55 An automobile with an initial speed of 4.30 m/s accelerates uniformly at the rate of 3.0 m/s 2. Find the displacement after 5.0 seconds. Δx = displacement=?? Vi = initial velocity= 4.30 m/s a = acceleration= 3.0 m/s^2 Δt = time interval= 5.0 s

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Solve! Plug in values and solve for displacement

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Final Velocity after any displacement V f = final velocity V i = initial velocity a = acceleration Δx = displacement

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Example: p.58 #3 A car accelerates uniformly in a straight line from rest at the rate of 2.3 m/s^2. What is the speed of the car after it has traveled 55 m? Vf = final velocity=?? Vi = initial velocity= rest= 0 m/s a = acceleration= 2.3 m/s^2 Δx = displacement= 55 m

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Solve

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Rearranging Your problems won’t always be so straightforward…make sure to rearrange your equations to solve for the unknown before plugging in your numbers (with units!)

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Section 2-3 Falling Objects Free Fall: Neglecting air resistance, all objects fall with the same constant acceleration

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Acceleration due to gravity

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Free Fall Acceleration However, acceleration is a vector. Gravity acts toward the earth (down) Therefore, the acceleration of objects in free fall near the surface of the earth is

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What we see because of air resistance…

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Object falling from rest

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Path of a projectile At top of path v= 0 m/s a = -9.81 m/s 2

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Free Fall Acceleration At the highest point of an arc, an object has velocity = 0 m/s, acceleration is still -9.81 m/s 2 An object thrown into the air is a freely falling body with

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Free Fall Problem p.64 #2 A flowerpot falls from a windowsill 25.0 m above the sidewalk A. How fast is the flowerpot moving when it strikes the ground? B. How much time does a paserby on the sidewalk below have to move out of the way before the flowerpot hits the ground?

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Part. A. What are we looking for: V f What do we know? Displacement: -25 m Acceleration: -9.81 m/s 2 V i =0 m/s What equation should we use??

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Solve the problem

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Part b. How much time before the flowerpot hits the ground? What do we know? Displacement= -25.0 m Acceleration = -9.81 m/s 2 V initial= 0 V final = -22.1 m/s What are we looking for: Time! Which equation should we use??

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Solve the Problem

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