What is the difference between a scalar and a vector?

Scalar – Magnitude only Vector – Magnitude and direction

You are traveling 0.8 m/s North. What is the magnitude of your velocity?

Magnitude is how much. 0.8 m/s

What is the resultant vector when the vectors below are added? 14 m/s 7 m/s

What is the resultant vector when the vectors below are added? 14 m/s 7 m/s 21 m/s

What is the resultant vector when the vectors below are added? 14 m/s 7 m/s

What is the difference between position and displacement?

Position where you are. Displacement – how far you have moved from a given location.

What is the difference between distance and displacement?

Distance – How far you moved total. Displacement – How far you moved from a given point.

Speed and Velocity 1.Define speed 2.Define velocity 3.What is the difference between speed and velocity?

1.Define speed – how fast 2.Define velocity – how fast & in what direction 3.What is the difference between speed and velocity? – velocity tells direction speed does not. 4.Velocity is vector 5.Speed is scalar

1.Give an example of speed 2.Give an example of velocity

1.Given an example of speed 25 m/s 2.Give an example of velocity 25 m/s north (must have direction)

Can I change my speed without changing my velocity? Can I change me velocity without changing my speed?

Can I change my speed without changing my velocity? No- Velocity is speed and direction. If speed changes velocity changes. Can I change me velocity without changing my speed?

Can I change me velocity without changing my speed? Yes – speed does not depend on direction. I can change direction (Velocity) but stay at same speed. 10 m/s

1.What is the formula for speed? 2.What is the formula for velocity?

1.What is the formula for speed? v= d/t 2.What is the formula for velocity? v= d/t

What is the velocity of an object that travels 100 meters North in 9.2 seconds? Indicate your answer as a vector.

What is the velocity of an object that travels 100 meters in 9.2 seconds? Indicate your answer as a vector. V = d/t = 100 m/9.2s = 10.9 m/s 10.9 m/s

What is the time needed to complete a 200 km trip when your average velocity is 42 km/hr @ 45 o North of East? Draw your velocity vector.

V = d/t  t = d/v = 200 km/ 42 km/hr = 4.76 hours = 45 o above the horizon

How far can an object traveling 12.2 m/s travel in 8.3 seconds?

V = d/t  d = V*t = 12.2 m/s * 8.3 s = 101.26 m

During a trip your initial velocity is 25 m/s East and your final velocity is 10 m/s West. What is your ΔV?

During a trip your initial velocity is 25 m/s East and your final velocity is 10 m/s West. What is your ΔV = V f – V i = -10 – 25 = -35 m/s Opposite directions (East/West) so one is positive and one is negative.

Speed/Velocity Use the equation below to answer the following questions v = d t 1.What is the velocity of a car who travels 100 m in 8 seconds? 2.How far can a vehicle traveling 23 m/s travel in 30 seconds? 3.How long will it take to drive 320 meters traveling at 24 m/s?

Speed/Velocity Use the equation below to answer the following questions v = d t 1.What is the velocity of a car who travels 100 m in 8 seconds?

Speed/Velocity Use the equation below to answer the following questions v = d t 1.How far can a vehicle traveling 23 m/s travel in 30 seconds?

Speed/Velocity Use the equation below to answer the following questions v = d t 1.How long will it take to drive 320 meters traveling at 24 m/s?

Not including the numbers, what is different about the graphs?

Position vs time Velocity vs time

What is the difference between instantaneous velocity and average velocity?

Instantaneous = at the exact time. Average = the average for the whole trip.

Which graph can tell you instantaneous velocity just by looking?

Which graph can tell you instantaneous velocity just by looking? Velocity vs. Time @ 3 seconds velocity is 12m/s

What item(s) in your car can be used to determine: Instantaneous velocity Average velocity

What item(s) in your car can be used to determine: Instantaneous velocity speedometer Average velocity Clock and odometer. Need time and distance. V = d/t

How far did the object travel during the first 2 seconds?

7.5 m (from 5 meters to 12.5 meters) Pay attention to where the graph starts

Speed/Velocity 1) Draw a POSITION VS. TIME graph which represents: –Constant positive velocity 2) Draw a VELOCITY VS. TIME graph which represents: –Constant positive velocity

Speed/Velocity Draw a graph which represents: –Constant positive velocity Position (x) meters Time (t) seconds Velocity m/s Time (t) seconds Any horizontal line above the y-axis will show constant positive velocity.

1) Draw a POSITION VS. TIME graph which represents: –No velocity and then –Constant positive velocity 2) Draw a VELOCITY VS. TIME graph which represents: –No velocity and then –Constant positive velocity

Draw a graph which represents: –No velocity and then const. + v Position (x) meters Time (t) seconds No velocity  no change in position Constant + velocity

1) Draw a POSITION VS. TIME graph which represents: –No velocity and then –Constant negative velocity 2) Draw a VELOCITY VS. TIME graph which represents: –No velocity and then –Constant negative velocity

Draw a graph which represents: –No velocity and then Constant negative velocity Position (x) meters Time (t) seconds Velocity m/s Time (t) seconds Any horizontal line below the y-axis will show constant negative velocity. Any horizontal line on the x-axis v=0

1) Draw a POSITION VS. TIME graph which represents: 2) Draw a VELOCITY VS. TIME graph which represents: –A car driving to school at 25 mph and then returning at 25 mph

Draw a graph which represents: –A car driving to school at 25 mph and then returning at 25 mph Position (x) meters Time (t) seconds The time spent at school. It is flat because your position is not changing. You are at school. Velocity m/s Time (t) seconds 1.Speed up to 25 mph 2.Drive at constant 25 mph 3.Slow down to 0 mph 4.Stay at school 5.Speed up to 25 mph (negative because go back home) 6.Constant speed (-25 mph) 7.Slow down and stop at home 1 2 3 4 5 6 7

1) Draw a POSITION VS. TIME graph which represents: 2) Draw a VELOCITY VS. TIME graph which represents: –A car driving to school at 30 mph and then returning at 15 mph

Draw a graph which represents: –A car driving to school at 30 mph and then returning at 15 mph Positi on (x) mete rs Time (t) seconds Slope of position versus time = velocity Less velocity on way home so less slope (Twice the time) Velocity m/s Time (t) seconds Positive 30 Negative 15 Twice as long Note the velocity vs time graph does not show the car speeding up, slowing down or stopping at school

1) Draw a POSITION VS. TIME graph that shows an object traveling: a)10 m/s from 0-1 seconds b)20 m/s from 1-2 seconds c)30 m/s from 2-3 seconds d)40 m/s from 3-4 seconds

1) Draw a POSITION VS. TIME graph that shows an object traveling: a)10 m/s from 0-1 seconds = 10 meters b)20 m/s from 1-2 seconds = 20 meters – 30 total c)30 m/s from 2-3 seconds = 30 meters – 60 total d)40 m/s from 3-4 seconds = 40 meters – 100 total Positi on (x) mete rs Time (t) seconds 12 34 20 40 60 80 Object is speeding up (accelerating) graph is exponential follows parabola

Speed/Velocity 1.A train travels 110 km from South Bend, IN to Chicago, IL in 45 minutes. The train must continue from Chicago to Milwaukee, WI, a distance of another 150 km. In what time must it travel from Chicago to Milwaukee in order to have the same average speed as the first part of the trip?

Define Acceleration What is the formula for acceleration

Define Acceleration – change in velocity (speed or direction) What is the formula for acceleration a = Δv/t

Car Ramp You have a yardstick and a stopwatch. 1.How can you calculate the final velocity of your car? 2.How can you calculate the average velocity of you car? 3.How can you calculate the acceleration of you car?

Which is a better definition of acceleration? Explain –Change in speed –Change in velocity

Which is a better definition of acceleration? Explain –Change in speed –Change in velocity Acceleration is a change in speed or direction. Velocity is speed in a direction

Complete the following table QuantityEquationUnits DistanceLeave Blank Acceleration Leave Blanks, hr m/s

QuantityEquationUnits DistanceLeave Blankm, km Accelerationm/s 2 timeLeave Blanks, hr velocitym/s

Which graph shows instantaneous velocity? Which graph shows average velocity?

Which graph shows instantaneous velocity? Top Which graph shows average velocity? bottom

Use terms constant, increase, decrease, positive, negative and 0 what is happening to the velocity from: 1)0 to 4 seconds? 2)4 to 6 seconds? 3)6 to 8 seconds? 4)8 to 10 seconds? 5)10 to 13 seconds?

What is happening from: 1)0 to 4 seconds? Constant + velocity 2)4 to 6 seconds? Zero velocity (at rest) 3)6 to 8 seconds? Constant - velocity 4)8 to 10 seconds? Rest (original position 5)10 to 13 seconds? Constant + velocity

What is the velocity from: 1)0 to 4 s? A.Is it constant? 2)4 to 6 s? A.Is it constant?

What is the velocity from: 1)0 to 4 m/s? rise over run = position over time = 8 m / 4 seconds = 2 m/s A.Is it constant? Yes, slope is constant 2)4 to 6 seconds? rise over run = position over time = 0 m / 4 seconds = 0 m/s A.Is it constant? Yes, slope is constant

1)Which segment(s) show constant velocity? 2)Which segment(s) show constant acceleration?

1)Which segment(s) show constant velocity? 3 to 5 velocity is 6 m/s 2)Which segment(s) show constant acceleration? All of them the slope is constant

1)What is the acceleration from 3 to 5 seconds? 2)What is the acceleration from 0 to 3 seconds? 3)What is the acceleration from 8 to 11 seconds?

1)What is the acceleration from 3 to 5 seconds? a = Δv/t = (v f –v i )/t = (6m/s–6m/s)/2s = (0 m/s)/2s= 0m/s 2 2)What is the acceleration from 0 to 3 seconds? a = Δv/t = (v f –v i )/t = (6m/s–3m/s)/3s = (3 m/s)/3s= 1m/s 2 2)What is the acceleration from 8 to 11 seconds? a = Δv/t = (v f –v i )/t = (Note: final – initial) (0m/s–9m/s)/3s = (-9 m/s)/3s= -3m/s 2 Slowing down = -acceleration

What is a vector? What is a scalar? What is the difference?

What is a vector? Magnitude and direction What is a scalar? Magnitude only (amount  25 m/s) What is the difference? Vectors have direction

Velocity is a vector or scalar? Speed is a vector or scalar? Acceleration is a vector or scalar?

Velocity is a vector or scalar? Direction Speed is a vector or scalar? No Direction Acceleration is a vector or scalar? Direction

Acceleration Calculate the time it takes for a car traveling 60 mph (88 fps) to stop. The stopping acceleration of a car is 15 ft/s 2.

The picture to the left shows a ball at 1 second increments. How do you know the ball is accelerating?

It is speeding up. It travels further every second.

What is the rate of acceleration due to gravity on Earth?

9.81 m/s 2  We will use g = 10 m/s 2

Complete the table to the left for object in free fall on earth. Time in free fall (s) Velocity (m/s) (Assume started from rest) 1 2 40 55

Complete the table to the left for object in free fall on earth. Time in free fall (s) Velocity (m/s) (Assume started from rest) 110 220 440 5.555

After disappointing seasons both players decide to jump at the same time (free fall). Who hits the ground first? Ryan Howard weighs 240 lbs. David Wright weighs 215 lbs.

After disappointing seasons both players decide to jump at the same time. Who hits the ground first? Ryan Howard weighs 240 lbs. David Wright weighs 215 lbs. They hit at the same time. Free fall – everything accelerates at 10 m/s 2. Goes faster and faster but hit at same time. No air resistance. (Assume a vacuum)

Which equation (1-6) should be used to solve the problem below: A meteor falls from the sky to the Earth. The meteor already had an initial velocity downward when it was spotted. If it hit the Earth at 335 m/s after being seen for 30 seconds, then what was the initial velocity of the meteor?

Which equation (1-6) should be used to solve the problem below: A meteor falls from the sky to the Earth. The meteor already had an initial velocity downward when it was spotted. If it hit the Earth at 335 m/s after being seen for 30 seconds, then what was the initial velocity of the meteor? Falling on earth a = g = - 10 m/s 2 v f = v i + aΔt

Which equation (1-6) should be used to solve the problem below: A baseball is thrown horizontally at 45 m/s. The ball slows down at a rate of 5 m/s2. How long is the ball in the air before coming to rest?

Which equation (1-6) should be used to solve the problem below: A baseball is thrown horizontally at 45 m/s. The ball slows down at a rate of 5 m/s 2. How long is the ball in the air before coming to rest? v f = v i + aΔt

Solve for a v f = v i + aΔt 2 m/s = 18 m/s + a(3s)

v f = v i + aΔt 2 m/s = 18 m/s + a(3s) Subtract 18 m/s from both sides -16 m/s = a(3s) Divide both sides by 3s -5.33 m/s 2 = a

Given initial velocity upwards of a projectile, and time in the air what equation would you use to solve for distance?

a = g = 10 m/s 2 Note v i (up) a (down) they need opposite signs one + and one -

What equation would you use to solve for time given an average speed and a distance?

Given an initial velocity and time in free fall what equation is used to solve for final velocity?

Free fall a = g= 10 m/s 2

What equation is used to solve for acceleration given distance traveled and final and initial velocities?

What equation is used to solve for a displacement over a given time with a known initial velocity and a known constant acceleration?

Note only the Δt is squared

Given an initial velocity a known constant acceleration and a time of acceleration what equation is used to solve for final velocity?

Given an initial velocity downward for an object in freefall and the time in freefall what equation is used to find the height of the fall?

Given an initial velocity upward of 5 m/s for an object in freefall and the time of 3 s in freefall what equation(s) could find the height of the fall?

Equation 2 or 3 (v i is up and g is down so need opposite signs)

Acceleration Complete the following for acceleration –Definition –Formula –Units

Acceleration Name the three items inside a car that the driver can use to accelerate the car.

Acceleration Name the three items inside a car that the driver can use to accelerate the car. Acceleration = change in speed or direction. Gas pedal, brake, steering wheel

Freefall Draw a picture of a ball in free fall. Show its position at 0 seconds, 1 second, 2 seconds and 3 seconds:

Freefall Draw a picture of a ball in free fall. Show its position at 0 seconds, 1 second, 2 seconds and 3 seconds: The object is accelerating at 10m/s 2 (Increase speed by 10m/s every second) So the distance the ball travels every second will be greater.

Freefall Draw a picture of a shot put in freefall next to the baseball.

Freefall Draw a picture of a shot put in freefall next to the baseball. Free fall  only gravity acting on the object. No air resistance. Will accelerate at 10m/s 2. All objects will speed up and speed up until they hit the ground at the same time.

The path to the left is the path of a ball thrown straight up that then falls back to earth in free fall. At each point indicate the direction of velocity and the direction of acceleration.

V = a = V = a = V = a = V = a = V = ? a =

Complete the velocity and acceleration velocities for the ball thrown upwards at 1 second intervals V = 20 m/s a = V = a = V = a = V = a = V = a =

Complete the velocity and acceleration velocities for the ball thrown upwards at 1 second intervals V = 20 m/s a = 10m/s 2 V = 10 m/s a = 10m/s 2 V = 10 m/s a = 10m/s 2 V = 20 m/s a = 10m/s 2 V = 0 m/s a = 10m/s 2

Rank greatest to least acceleration

Velocity Each diagram shows a ball traveling from left to right. The position of the ball each second is indicated by the second. Rank the VELOCITY from greatest to least indicated in each diagram. Right is positive and left is negative.

Acceleration Each diagram shows a ball traveling from left to right. The position of the ball each second is indicated by the second. Rank the ACCELERATION from greatest to least indicated in each diagram. Right is positive and left is negative.

Speed/Velocity/Acceleration Circle the point(s) on the graph where the object has 0 velocity :

Speed/Velocity/Acceleration Circle the point(s) on the graph where the object has 0 acceleration:

Create a position vs. time graph that shows an object: 1.Leaving position 0 with a constant velocity of 4 m/s for 8s 2.At rest for 2 seconds 3.With constant negative velocity back to position 0 in 16 seconds. What is the velocity for this segment?

Create a position vs. time graph that shows an object: 1.Leaving position 0 with a constant velocity of 4 m/s for 8s v = d/t  4 m/s = d/8s  d = 4 m/s * 8 s = 32 m 2.At rest for 2 seconds No position change only time change of 2 s. 3.With constant negative velocity back to position 0 in 16 seconds. (Took twice as long so ½ the original velocity = 2 m/s in opposite direction -2 m/s)

Speed/Velocity WHEN THE 10 km/h BIKES ARE 20 km APART, A BEE BEGINS FLYING FROM ONE WHEEL TO THE OTHER AT A STEADY SPEED OF 30 km/h. WHEN IT GETS TO THE WHEEL, IT ABRUPTLY TURNS AROUND AND FLIES BACK TO TOUCH THE FIRST WHEEL, THEN TURNS AROUND AND KEEPS REPEATING THE BACK-AND-FORTH TRIP UNTIL THE BIKES MEET, AND "SQUISH!" How many km’s did the bee travel back-and- forth before being squished?

Acceleration Calculate the acceleration of a car that goes from 0 to 60 mph in 5.6 seconds.

Acceleration The fastest recorded speed for high speed rail is 357.2 mph (523.9 fps). Assuming the same stopping time (5.87 seconds) and acceleration (15 fps), what is the velocity of the train after the car in the last problem has stopped. Convert your answer to miles per hour.

What segment shows 1)Greatest distance from starting point? 2)Greatest velocity? 3)Least velocity? 4)Least speed?

What segment shows 1)Greatest distance from starting point? 13 seconds 2)Greatest velocity? 10 to 13 (d/t = 12m/3s = 4 m/s) 3)Least velocity? 6 to 8 (-8m/2s = -4 m/s) 4)Least speed? 4 to 6 and 8 to 10 (O m/s) no direction with speed

1)Which segment(s) show 0 acceleration? 2)Which segment(s) show the greatest acceleration? 3)Which segment(s) show the least acceleration?

1)Which segment(s) show 0 acceleration? 3 to 5 (0 slope) 2)Which segment(s) show the greatest acceleration? 0 to 3 and 5 to 8 (Δv/t = (6-3)/3 = 1 m/s 2 ) 3)Which segment(s) show the least acceleration? 8 to 11 ((0-9)/3 = -3 m/s 2

Acceleration Explain the difference in physics between acceleration and deceleration

Acceleration The cheetah can accelerate from 0 to 60 mph in 3 seconds. Your car has a top speed of 45 mph. In order to accelerate at the same rate of the cheetah how quickly do you have to reach your top speed?

Acceleration The cheetah can accelerate from 0 to 60 mph in 3 seconds. Your first car has a top speed of 45 mph. In order to accelerate at the same rate of the cheetah how quickly do you have to reach your top speed?

Speed/Velocity/Acceleration What is the velocity of the object depicted in the graph:

Speed/Velocity/Acceleration Explain how you determined the object below is accelerating:

Speed/Velocity/Acceleration Calculate the distance the object traveled in the first 30 minutes:

Motion Define the following terms –Scalar –Vector

Motion Define the following terms –Displacement –Position

What is the difference between a scalar and a vector?

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What is the difference between a scalar and a vector?

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