LEARNING TARGET 4: ACCELERATION 4.1 I can calculate final speed given initial speed and acceleration 4.2 I can calculate acceleration given change in speed and time 4.3 I can calculate time given speed and distance 4.4 I can interpret and sketch a velocity vs time graph

Acceleration Definition: Change in velocity

Speed vs. Velocity Revisited Speed = how fast on object is moving Velocity = how fast an object is moving in a certain direction speeddirection Velocity

Acceleration Definition: Change in velocity ◦ Can be change in speed OR direction ◦ (speed up, slow down, or change direction)

Is this ball accelerating?? Yes! Because it is changing direction!

Quick Checks What is acceleration? Acceleration can be a change in ____ or ____. Is there acceleration in these situations? Why? A car speeding from red light to red light. A car on the freeway. A pendulum A car doing donuts.

Which cars are accelerating? Cars B and C! A B C

Acceleration Acceleration is not just a change in velocity, it’s how fast that change happens.

Which car has the greatest acceleration? Car C! A B C

Acceleration To measure it, you must know the initial velocity, the final velocity, and the time it takes to make the change.

Acceleration Definition: Change in velocity ◦ Can be change in speed or direction ◦ (speed up, slow down, or change direction) Acceleration = ∆v/t

Acceleration  - Greek letter delta – “change in”  v is the difference between the final velocity (v f ) and the initial velocity (v i ). Initial Velocity (v i ) – An object’s velocity when you start measuring acceleration Final Velocity (v f ) – An object’s velocity when you finish measuring acceleration Δ v = v f - v i

Acceleration Definition: Change in velocity ◦ Can be change in speed or direction ◦ (speed up, slow down, or change direction) Acceleration = ∆v/t ◦ ∆v = v f – v i

Acceleration Positive acceleration = speeding up Negative acceleration = slowing down

Practice! A roller coaster’s velocity at the top of a hill is 10m/s. Two seconds later it reaches the bottom of the hill with a velocity of 26m/s. What is the acceleration of the roller coaster?

Use GUESS! G: v f = 26 m/s v i = 10 m/s t = 2 s U: acceleration E: acceleration = ∆v/ t S: a = 26m/s – 10m/s 2 s S: a = 16m/s 2s a = 8m/s/s or 8m/s 2 A roller coaster’s velocity at the top of a hill is 10m/s. Two seconds later it reaches the bottom of the hill with a velocity of 26m/s. What is the acceleration of the roller coaster?

Quick Checks 1. A car travels at 60 miles per hour around a curve. Is the car accelerating? 2. A car travels in a straight line at 60 mi/hr. Is the car accelerating? 3. A car goes from 0 m/s to 60 m/s in 6 seconds. What’s the car’s acceleration?

Let’s make it a bit harder… If a Ferrari, with an initial velocity of 10 m/s, accelerates at a rate of 50 m/s 2 for 3 seconds, what would its final velocity be?

Use GUESS! G: a = 50 m/s 2 v i = 10 m/s t = 3 s U: final velocity E: acceleration = Δv/t S: 50 m/s 2 = v f – 10 m/s 3 s S: v f = (50 m/s 2 x 3s) + 10 m/s v f = 160 m/s

Practice! 1. The velocity of a car increases from 2m/s at 1s to 16m/s at 4.5s. What is the car’s average acceleration? 2. Monica starts running from rest to a velocity of 7m/s. It takes her a total of 8s. What is her acceleration? 3. A shuttle bus slows to a stop with an average acceleration of -1.8 m/s 2. How long does it take the bus to slow down from 9.0 m/s to 0.0 m/s? 4. With an average acceleration of m/s 2, how long will it take a cyclist to bring a bicycle with an initial speed of 13.5 m/s to a complete stop?

Practice! The velocity of a car increases from 2m/s at 1s to 16m/s at 4.5s. What is the car’s average acceleration?

Practice! Monica starts running from rest to a velocity of 7m/s. It takes her a total of 8s. What is her acceleration?

Practice! A shuttle bus slows to a stop with an average acceleration of -1.8 m/s 2. How long does it take the bus to slow down from 9.0 m/s to 0.0 m/s?

Practice! With an average acceleration of m/s 2, how long will it take a cyclist to bring a bicycle with an initial speed of 13.5 m/s to a complete stop?

Constant Velocity CONSTANT VELOCITY = NO CHANGE IN VELOCITY Definition of acceleration = CHANGE IN VELOCITY over a period of time CONSTANT VELOCITY = 0 ACCLERATION

Position vs. Time Graphs Straight line = Constant motion Curved line = Accelerated motion

Velocity vs. Time Graphs What is in a velocity vs. time graph? X-axis: time (s) that the object is in motion Y-axis: velocity (m/s) of the object in motion SLOPE = ACCELERATION of the object

Velocity vs. Time Graphs Slope = rise = Δ y run Δ x = How much your VELOCITY is changing How much your time is changing = ∆v = acceleration! ∆t

PointVelocity Q R S T U

Between which letters is velocity increasing? Between which letters is velocity decreasing? Between which letters is velocity constant?

When velocity increases, the acceleration is: When the velocity decreases, the acceleration is: When the velocity remains constant, the acceleration is:

PointAcceleration Q – R R – S S – T T – U

Position vs. Time VERSUS Velocity vs. Time Position vs. Time GraphVelocity vs. Time Graph X-axis Y-axis Slope Steeper line means… Horizontal line means… Downward sloping line means… Time (s) Position (m)Velocity (m/s) Acceleration (m/s2) Faster velocity Speeding up No velocity = at rest Constant velocity = no acceleration Moving backwards Slowing down

Create the matching velocity vs. time graph:

Visualizing Motion with Constant Acceleration Motion diagrams for three carts: An acceleration of 0 m/s 2 tells you the velocity will remain the same each second of the motion. Acceleration tells you the amount by which the velocity will increase (+a) or decrease (-a) each second of the motion.

One-Dimensional Motion with Constant Acceleration Constant or uniform acceleration means that the velocity increases or decreases at the same rate throughout the motion. ◦ The rate of change in the velocity is always the same. Variables to consider: ◦ x i = initial displacement ◦ x f = final displacement ◦ v i = initial velocity ◦ v f = final velocity ◦ a = acceleration ◦ t = time

Kinematic Equations Use with constant acceleration Δx =½(V i + V f )t Δx= V i (t) + ½at 2 V f = V i + at V f 2 = V i 2 +2aΔx

Kinematic example 1 When Maggie applies the brakes of her car, the car slows uniformly from 15m/s to 0m/s in 2.5 s. How many meters before a stop sign must she apply her brakes in order to stop at stop sign? 2c pg 53- #2 Given: Unknown: Drawing: Equation: Solve:

Kinematic example 2 A car starts from rest and travels for 5.0s with a uniform acceleration of -1.5m/s 2. What is the final velocity of the car? How far does the car travel in this time interval? 2d pg 55 #3 Given: Unknown: Drawing: Equation: Solve:

Kinematic example 3 A baby Sitter pushing a stroller starts from rest and accelerates at a rate of 0.500m/s 2. What is yhr vrlocity of the stroller after it has travelled 4.75m? Pg 57 example Given: Unknown: Drawing: Equation: Solve: