Force and Motion Unit

Horizontal Acceleration

1ObjectivesI 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 objects velocity.Horizontal Acceleration

3Changes in DirectionAcceleration 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:

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Changes in Speed and DirectionSometimes 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 . . .

5Turn 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:

7Constant AccelerationThe 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 airplanes acceleration may be constant during a portion of its takeoff.

8Acceleration is the rate at which velocity changes. Calculating Acceleration

Vi is the initial velocity vf is the final velocity t is total time.

Entire equation in symbols:a = vf vi t

9Explain to the students that scientists use symbols all the time so they dont have to write out all the words!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

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Givens: 2 s = starting from rest means?6 m/s = tvi = 0vf Unknown =a Equation =a = vf vi 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 s2

11Walk the students through this step by step. Have them tell you what variable to use for each number.

On the answer portion: explain how the s in the m/s goes on the bottom, then how a s times a s = a second squaredIndependent PracticeFor extra practice on your own Math page 348 #8 & #9(optional)

You can have students do this in a notebook or on a separate sheet of paper to hand in.12

Vertical Acceleration

13Objectives 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/s2). Objects falling near Earths surface accelerate downward at a rate of 9.8 m/s2. Vertical Acceleration

15Each second an object is in free fall, its velocity increases downward by 9.8 meters per second. The change in the stones speed is 9.8 m/s2, the acceleration due to gravity.What Is Acceleration?

t = 0 sv = 0 m/st = 1 sv = 9.8 m/st = 2 sv = 19.6 m/st = 3 sv = 29.4 m/s

16Final Velocity Equation for a Dropped Object

Equation: vf = vi + at a = acceleration (unit m/s2)vf = final velocity (unit m/s)vi = initial velocity (unit m/s)(vi 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

18Givens: 2 s = What is the initial velocity?tvi = 0vf Unknown =Equation =a = vf vi t Plug it in =Answer =vf = 19.6 m/s Any time you drop something, what variable can you use?g = 9.8 m/s2Rearranged:vf = vi + at vf = 0 + (9.8 m/s2)(2s) 19Walk the students through this step by step. Have them tell you what variable to use for each number.

On the answer portion: explain how one of the s in s2 is canceled out by the s on the topTurn to a partner practiceExplain a situation in which you can accelerate even though your speed doesnt change.Find the final velocity of a book dropped from cliff at a time frame of 3.8 seconds.

20Turn to a partner practice-- answerExplain a situation in which you can accelerate even though your speed doesnt change.2. Find the final velocity of a book dropped from cliff at a time frame of 3.8 seconds.ANSWER: A car turn a corner. (Any situation where you are changing direction.)Givens: 3.8 s = tKnow: g = 9.8 m/s2 vi = 0 m/sUnknown: vfEquation: vf = vi + gtPlug in numbers: vf = 0 m/s + (9.8 m/s2)(3.8 s) Answer: 37.24 m/s

21You 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

22The skiers acceleration is positive. Find the acceleration (slope).Lets Practice! Graphs of Accelerated Motion

23The skiers acceleration is positive. Find the acceleration (slope).Graphs of Accelerated Motion -- answer

a = vf vi t a = 16 m/s 0 m/s 4 s 0 m/sa = 4 m/s2

24Remind students that the acceleration equation is just like the slope of a line equation y2 y1 over x2 x1!Speed-Time GraphsConstant acceleration is represented on a speedtime 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

25Constant 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

26The biker moves at a constant speed and then slows to a stop.

What is the bikers constant speed?What is the bikers deceleration?Graphs of Accelerated Motion Turn to a partner

27The biker moves at a constant speed and then slows to a stop.

What is the bikers constant speed? 5 m/sWhat is the bikers deceleration? 0 m/s 5 m/s = 0.5 m/s2 20 s 10 sGraphs of Accelerated Motion Turn to a partner Answers

28Assessment Question #1What is acceleration? the rate at which speed increasesthe time an objects velocity increasesthe rate at which displacement changesthe rate at which velocity changes

29Assessment Question #1 answerWhat is acceleration? the rate at which speed increasesthe time an objects velocity increasesthe rate at which displacement changesthe rate at which velocity changes

ANS:D

30Assessment Question #2A sports car can accelerate from 0m/s to 28m/s in fourseconds. What is the acceleration of the car?24s7m/s27m/s27m/s

31Assessment Question #2 -- answerA sports car can accelerate from 0m/s to 28m/s in fourseconds. What is the acceleration of the car?24s7m/s27m/s27m/s

ANS:C 32Assessment Question #33. Which of the following is an example of negative acceleration? Mike starts riding his bike and uses the pedals to go from 0 km/h to 20 km/h.Mike pedals up a hill and gradually slows from 20 km/h to 5 km/h.Mike sits on his bike at the top of the hill and rests.Mike coasts downhill without pedalling, going from 0 km/h to 15 km/h.

33Assessment Question #3 -- answer3. Which of the following is an example of negative acceleration? Mike starts riding his bike and uses the pedals to go from 0 km/h to 20 km/h.Mike pedals up a hill and gradually slows from 20 km/h to 5 km/h.Mike sits on his bike at the top of the hill and rests.Mike coasts downhill without pedalling, going from 0 km/h to 15 km/h.

ANS:B 34Assessment Question #44. If an object experiences a steady velocity change in a straight line, it is undergoing constant acceleration.

TrueFalse

35Assessment Question #4 -- answer4. If an object experiences a steady velocity change in a straight line, it is undergoing constant acceleration.

TrueFalse

ANS:T 36HomeworkWrite a paragraph on terminal velocity. (You must define it and explain how it relates to a sport.)

From Wikipedia:

A free-falling object achieves its terminal velocity when the downward force of gravity (FG) equals the upward force of drag (Fd). This causes the net force on the object to be zero, resulting in an acceleration of zero.

Based on wind resistance, for example, the terminal velocity of a skydiver in a belly-to-earth (i.e.:face down) free-fall position is about 195km/h (122mph or 54m/s).[2] This velocity is the asymptotic limiting value of the acceleration process, because the effective forces on the body balance each other more and more closely as the terminal velocity is approached. In this example, a speed of 50% of terminal velocity is reached after only about 3 seconds, while it takes 8 seconds to reach 90%, 15 seconds to reach 99% and so on.Higher speeds can be attained if the skydiver pulls in his or her limbs (see also freeflying). In this case, the terminal velocity increases to about 320km/h (200mph or 90m/s),[2] which is almost the terminal velocity of the Peregrine Falcon diving down on its prey.[3] The same terminal velocity is reached for a typical .30-06 bullet dropping downwardswhen it is returning to earth having been fired upwards, or dropped from a toweraccording to a 1920 U.S. Army Ordnance study.[4]Competition speed skydivers fly in the head down position and reach even higher speeds. The current world record is 614mph (988km/h) by Joseph Kittinger, set at high altitude where the lesser density of the atmosphere decreased drag.[2]

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