Horizontal Acceleration

Objectives I will know how motion changes with respect to acceleration. I will be able to solve horizontal acceleration story problems.

In science, acceleration applies to any change in velocity. Acceleration can be caused by positive (increasing) change in velocity or by negative (decreasing) change in velocity. Deceleration is an acceleration that slows an object’s velocity. Horizontal Acceleration

Changes in Direction Acceleration can be the result of a change in direction at constant speed. Examples: Riding a bicycle around a curve A horse on the carousel is traveling at a constant speed, but it is accelerating because its direction is constantly changing. Acceleration also involves:

Changes in Speed and Direction Sometimes motion is characterized by changes in both speed and direction at the same time. Passengers in a car moving along a winding road experience rapidly changing acceleration. The car may enter a long curve at the same time that it slows. The car is accelerating both because it is changing direction and because its speed is decreasing. OR...

Turn to a partner: Discuss other situations with horizontal acceleration.

A roller coaster produces acceleration due to changes in both speed and direction. Turn to a partner possible answer:

Constant Acceleration The velocity of an object moving in a straight line changes at a constant rate when the object is experiencing constant acceleration. Constant acceleration is a steady change in velocity. An airplane’s acceleration may be constant during a portion of its takeoff.

Acceleration is the rate at which velocity changes. Calculating Acceleration V i is the initial velocity v f is the final velocity t is total time. Entire equation in symbols: a = v f – v i t

A ball rolls down a ramp, starting from rest. After 2 seconds, its velocity is 6 meters per second. What is the acceleration of the ball? Calculating Acceleration Practice Problem

Givens: 2 s = starting from rest means? 6 m/s = t v i = 0 vfvf Unknown = a Equation = a = v f – v i t Plug it in = a = 6 m/s – 0 m/s 2 s Answer = a = 3 m/s s a = 3 m s ∙ s a = 3 m s 2

Independent Practice For extra practice on your own Math page 348 #8 & #9 (optional)

Vertical Acceleration

Objectives Day 4 I will know the difference between horizontal and vertical acceleration. I will be able to solve vertical acceleration problems. I will be able to read and interpret data and graphs.

Free fall is the movement of an object toward Earth solely because of gravity. The unit for velocity is meters per second. The unit for acceleration, then, is meters per second per second. This unit is typically written as meters per second squared (m/s 2 ). Objects falling near Earth’s surface accelerate downward at a rate of 9.8 m/s 2. Vertical Acceleration

Each second an object is in free fall, its velocity increases downward by 9.8 meters per second. The change in the stone’s speed is 9.8 m/s 2, the acceleration due to gravity. What Is Acceleration? t = 0 s v = 0 m/s t = 1 s v = 9.8 m/s t = 2 s v = 19.6 m/s t = 3 s v = 29.4 m/s

Final Velocity Equation for a Dropped Object Equation: v f = v i + at a = acceleration (unit m/s 2 ) v f = final velocity (unit m/s) v i = initial velocity (unit m/s) (v i will generally be zero unless you give it an initial velocity) t = time (unit s)

A child drops a ball from a bridge. The ball strikes the water under the bridge 2.0 seconds later. What is the velocity of the ball when it strikes the water? Calculating Acceleration – Modeled Practice

Givens: 2 s = What is the initial velocity? t v i = 0 vfvf Unknown = Equation = a = v f – v i t Plug it in = Answer = v f = 19.6 m/s Any time you drop something, what variable can you use? g = 9.8 m/s 2 Rearranged: v f = v i + at v f = 0 + (9.8 m/s 2 )(2s)

Turn to a partner practice 1.Explain a situation in which you can accelerate even though your speed doesn’t change. 2.Find the final velocity of a book dropped from cliff at a time frame of 3.8 seconds.

Turn to a partner practice -- answer 1.Explain a situation in which you can accelerate even though your speed doesn’t change. 2. Find the final velocity of a book dropped from cliff at a time frame of 3.8 seconds. ANSWER: 1.A car turn a corner. (Any situation where you are changing direction.) 2.Givens: 3.8 s = t Know: g = 9.8 m/s 2 v i = 0 m/s Unknown: v f Equation: v f = v i + gt Plug in numbers: v f = 0 m/s + (9.8 m/s 2 )(3.8 s) Answer: m/s

You can use a graph to calculate acceleration. Graph speed on the vertical axis and time on the horizontal axis. The slope is change in speed divided by change in time, which is equal to the acceleration. Graphs of Accelerated Motion

The skier’s acceleration is positive. Find the acceleration (slope). Let’s Practice! Graphs of Accelerated Motion

The skier’s acceleration is positive. Find the acceleration (slope). Graphs of Accelerated Motion -- answer a = v f – v i t a = 16 m/s – 0 m/s 4 s – 0 m/s a = 4 m/s 2

Speed-Time Graphs Constant acceleration is represented on a speed–time graph by a straight line. The graph is an example of a linear graph, in which the displayed data form straight-line parts. Graphs of Accelerated Motion

Constant negative acceleration decreases speed. On a speed-time graph of a bicycle slowing to a stop, a line sloping downward represents the bicycle decelerating. The change in speed is negative, so the slope of the line is negative. Graphs of Accelerated Motion

The biker moves at a constant speed and then slows to a stop. 1.What is the biker’s constant speed? 2.What is the biker’s deceleration? Graphs of Accelerated Motion – Turn to a partner

The biker moves at a constant speed and then slows to a stop. 1.What is the biker’s constant speed? 5 m/s 2.What is the biker’s deceleration ? 0 m/s – 5 m/s = 0.5 m/s 2 20 s – 10 s Graphs of Accelerated Motion – Turn to a partner Answers

Assessment Question #1 1.What is acceleration? a.the rate at which speed increases b.the time an object’s velocity increases c.the rate at which displacement changes d.the rate at which velocity changes

Assessment Question #1 answer 1.What is acceleration? a.the rate at which speed increases b.the time an object’s velocity increases c.the rate at which displacement changes d.the rate at which velocity changes ANS:D

Assessment Question #2 2.A sports car can accelerate from 0 m/s to 28 m/s in four seconds. What is the acceleration of the car? a.24 s b.7 m/s c.27 m/s d.27 m/s

Assessment Question #2 -- answer 2.A sports car can accelerate from 0 m/s to 28 m/s in four seconds. What is the acceleration of the car? a.24 s b.7 m/s c.27 m/s d.27 m/s ANS:C

Assessment Question #3 3. Which of the following is an example of negative acceleration? a.Mike starts riding his bike and uses the pedals to go from 0 km/h to 20 km/h. b.Mike pedals up a hill and gradually slows from 20 km/h to 5 km/h. c.Mike sits on his bike at the top of the hill and rests. d.Mike coasts downhill without pedalling, going from 0 km/h to 15 km/h.

Assessment Question #3 -- answer 3. Which of the following is an example of negative acceleration? a.Mike starts riding his bike and uses the pedals to go from 0 km/h to 20 km/h. b.Mike pedals up a hill and gradually slows from 20 km/h to 5 km/h. c.Mike sits on his bike at the top of the hill and rests. d.Mike coasts downhill without pedalling, going from 0 km/h to 15 km/h. ANS:B

Assessment Question #4 4. If an object experiences a steady velocity change in a straight line, it is undergoing constant acceleration. True False

Assessment Question #4 -- answer 4. If an object experiences a steady velocity change in a straight line, it is undergoing constant acceleration. True False ANS:T

Homework Write a paragraph on terminal velocity. (You must define it and explain how it relates to a sport.)