Name:__________________________Physics Chapter 2 Study GuideUseful Information:

a=v f−vit

x=(v f+vi2 )t x=vi t+12a t2 v f

2=vi2+2a x g=−9.81m

s2

A Basic Understanding:•Chapter 2 Odd Numbered Core Problems•Chapter 2 Review Problems: 3, 7, 12, 14, 16, 23, 26, 28, 30, 37, 42, 45.•Measuring Gravity parts A - E done correctly, if not neatly.•Graph Interpretation problems 1, 2.

Pushing to be Better:•Chapter 2 Your Try Problems•Chapter 2 Even Numbered Core Problems•Chapter 2 Review Problems: 1, 2, 4, 10, 11, 17, 19, 21, 22, 25, 32, 33, 36, 41, 47.•Standardized Test Prep 1-9.•Measuring Gravity all parts done both neatly and correctly.•Graph Interpretation problems 3, 4.

Digging Deeper:•Chapter 2 Review Problems: 34, 35, 50, 51•Explain clearly why problem 51 is poorly worded and has no precise solution.•Problem 34: use the graph to write the equation for the parabola. Use calculus to determine the acceleration.•Answers to your try questions on my worked examples sheet.•Individual Inquiry

Notes on Equations:

x - distance measured in meters.t - time measured in seconds.vi - initial velocity measured in meters per second.v f - final velocity measured in meters per second.a - acceleration measured in meters per second squared.

Learn that the acceleration due to gravity is -9.81 m/s2.

The equations as given on page 854 are a more precise and accurate expression of what is going on. I have made the equations less accurate and precise by eliminating some deltas and “avg.” But, hopefully, I have made them easier for you to remember.

The key to these four equations is that each equation is missing one of the variables. You will need to know three variables to solve for a fourth. Figure out what variable you can neglect andchoose the equation that does not contain that variable. Remember some quantities may be im-plicit; e.g. a dropped ball has an initial velocity of zero meters per second.

Physics Ch. 2 Study Guide page 1 of 1

Name:_____________________________Chapter 2 Worked Examples Physics1) A penny is thrown straight up from a balcony that is 4.15m above the sidewalk. The initial velocity of the penny is 10.0 m/s.

a) What is the maximum height of the penny above the sidewalk?b) How much time does it take for the penny to hit the sidewalk?c) What is the velocity of the penny when it hits the sidewalk.

Your Try: A baseball is thrown straight down from a balcony that is 9.75m above the sidewalk. It takes 0.75 seconds for the ball to hit the sidewalk.

a) What is the initial velocity of the baseball?b) What is the final velocity of the baseball?

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2) A ball is thrown upwards with an initial speed of 15.0 m/s. 2.00 seconds later, a second ball is thrown upwards with an initial speed of 10.0 m/s. At what height will they pass each other?

Your Try: A penny is dropped from a balcony that is 11.2 m above the sidewalk. At exactly the same time, a baseball is thrown upwards from the sidewalk with a speed of 8.50 m/s. How much time will elapse before they pass each other?

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3) A steep road has a constant grade of 13%. Which means that it has an angle of 7.4°. A car starts from rest at the bottom of the hill, accelerates up the hill at 2.34 m/s2 for 9.45 seconds. Then it runs out of gas and coasts to a stop. How far up the hill does the car get?

Your Try: A road biker starts from rest at the top of a hill that has an angle of 6.0°. They coast for 85.0 meters and then apply the brakes. It takes them 8.4 seconds to stop.How far do they travel between when they apply the brakes and when they come to a stop?

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Physics Chapter 2 Your Try Problems (Based on various worked examples.)1) Worked Example 1: A baseball is thrown straight down from a balcony that is 9.75m above the sidewalk. It takes 0.75 seconds for the ball to hit the sidewalk. a) What is the initial velocity of the baseball? b) What is the final velocity of the baseball?

2) Worked Example 2: A penny is dropped from a balcony that is 11.2 m above the sidewalk. At exactly the same time, a baseball is thrown upwards from the sidewalk with a speed of 8.50 m/s. How much time will elapse before they pass each other?

3) Worked Example 3: A road biker starts from rest at the top of a hill that has an angle of 6.0°. She coasts for 85.0 meters and then applies the brakes. It takes her 8.4 seconds to stop. How far does she travel between when she applies the brakes and when she comes to a stop?

4) Videos 2b&c:A person driving into a town is going 40mph when they pass the 40mph sign. And then

they are going 30mph when they pass the 30mph sign. The two signs are 0.25 miles apart. a) What is the average acceleration of the car, in meters per second?b) What is the time that it takes for the car to drive between the two signs?

5) Videos 2e,f&LYou are riding your road bike at 9m/s up a smooth road that is inclined at 15°. Ignore

friction. When you shift gears, your chain comes off. a) How much time do you have before you come to a complete stop and fall over (because you can’t clip-out).b) How much distance do you cover during this time?

6) Video 2hTwo people are exploring a cave with climbing equipment. They have a 60m long rope.

They come to a vertical shaft that they can’t see down. They drop a rock and hear it hit bottom 3 seconds later. Can they get down to where the rock hit with just one length of their rope?

7) Video 2jA person is standing on a balcony. They throw a ball up with an initial speed of 12 m/s.

3.8 seconds later, the ball hits the sidewalk at the base of the building.a) How high is the balcony?b) What is the velocity of the ball when it strikes the sidewalk?c) What is the maximum height of the ball above the balcony?

8) Video 2kA ball is thrown up with a speed of 15m/s. 0.75 seconds later, a second ball is thrown up

with a speed of 25m/s. At what height do they meet?

Answers to Chapter 2 Your Try Problems 1) Worked Example 1: A baseball is thrown straight down from a balcony that is 9.75m...

vi = - 9.3 ms

v f = - 16.7 ms

2) Worked Example 2: A penny is dropped from a balcony that is 11.2 m...

t =1.3s

3) Worked Example 3: A road biker starts from rest at the top...

x = 55.4m

4) Videos 2b&c: A person driving into a town is going 40mph...

a = - 0.17 ms2

t = 25.7s

5) Videos 2e,f&L: You are riding your road bike at 9m/s...

t = 3.5sx =16m

6) Video 2h: Two people are exploring a cave with climbing equipment...The drop is around 44m. They should have approximately 15 meters of rope more than they need.

7) Video 2j: A person is standing on a balcony. They throw a ball up...

a) 25.2mb) - 25.3 m

s

c) 7.3m

8) Video 2k: A ball is thrown up with a speed of 15m/s...

x =11m

Name:__________________________Physics Chapter 2 Core Problems

1) Consider the Displacement versus Time graph shown above.a) When is the object the furthest from its starting point?b) Does the object ever return to its starting point?c) When does the object have a maximum speed?d) When does the object have a minimum speed?e) When does the object have a maximum acceleration?f) When does the object have zero acceleration?

2) Consider the Velocity versus Time graph show above.a) When does the object have the highest speed?b) When is the object not moving?c) Rank the segments in order of highest acceleration to lowest acceleration.d) How far is the object from the starting point after 7 seconds?e) How far is the object from the starting point after 12 seconds?

Physics Ch. 2 Core Problems page 1 of 2

3) A car is traveling down the road at 22 m/s. It then accelerates to 31 m/s in 7.0 s. a) What is the average acceleration of the car during this 7.0 s interval?b) How far does the car travel during this 7.0 s interval?

4) A ball starts from rest and rolls down a ramp. At the bottom of the ramp the velocity of the ball is 3.6 m/s. The ramp is 2.5 m long. a) What is the average acceleration of the ball?b) How much time does it take for the ball to reach the bottom of the ramp?

5) Sally travels by car from one city to another. She drives for 30.0 min at 80.0 km/h, 12.0 min at 105 km/h, and 45.0 min at 40.0 km/h, and she spends 15.0 min eating lunch and buying gas.a) Determine the total distance traveled.b) Determine the average speed for the trip.

6) A penny is dropped from a balcony that is 11.2 m above the sidewalk. At exactly the same time, a baseball is thrown upwards from the sidewalk with a speed of 8.50 m/s. At what heightwill their paths cross?

Physics Ch. 2 Core Problems page 2 of 2

Name:_____________________________Measuring Gravity PhysicsA: Use a board to set up an incline. From the dimensions of the incline (rise, run, length) calcu-late the angle of the incline.

B: Start with the bottom edge of the cart 1 meter from the bottom of the ramp. Measure the time that it takes for the cart to run 1 meter down the incline. Repeat each trial 3 times, record each trial and average the results. Plug the distance and time into the appropriate equation to calculate the acceleration.

C: Place a brick on the cart and repeat part B.

D: Change the angle of the incline and repeat parts A-C.

E: Change the angle of the incline again and repeat parts A-C.

F: Using what you have observed from part II and what you know about triangles (sines, cosines, tangents, etc...) find a way to calculate the acceleration of a freely falling object. All of your data from part II is of critical importance in this. I want a calculation, not a number from a book. Was the addition of a brick significant?

Physics Measuring Gravity page 1 of 1

Name:_____________________________

Graph Interpretation Physics

1) The graph below is a not very realistic Distance versus Time graph for an object.a) Write a paragraph describing the graph in words.b) Write a paragraph describing the velocity of the object shown in this graph.

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2) The graph looks the same, but it's different. It is now a Velocity versus Time graph for an object.a) Write a paragraph describing the graph in words.b) Write a paragraph describing the acceleration of the object shown in this graph.c) Write a paragraph describing the displacement of the object shown in this graph.

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3) This is a more realistic graph of Distance versus Time.a) On what intervals does the object have a positive velocity?

b) On what intervals does the object have zero velocity?

c) On what intervals does the object have negative velocity?

d) Order the marked points according to when the particle's speed is greatest and when it is least.

e) On what intervals does the object have a positive acceleration?

f) On what intervals does the object have zero acceleration?

g) On what intervals does the object have negative acceleration?

h) Where does the object have its maximum acceleration?

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4) Below is a Velocity versus Time graph.a) On what intervals does the object have a positive acceleration?

b) On what intervals does the object have zero acceleration?

c) On what intervals does the object have negative acceleration?

d) Where is the acceleration of the object the greatest?

e) At what point is the object the furthest from its starting point?

Advanced: Write a paragraph explaining why the graphs in problems 3 and 4 are more realistic that the graphs in problems 1 and 2.

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