Chapter 2 Homework #1 Questions: 2,3,4,5,6,9,16, 17 Problems: 1,2,5,6,9,8,13, 17, 20,22,23,26, 27,28 Due Sept 29 Quiz on Section 1-6 on Sept 29

Physics Ch. 2 Motion in One Dimension Section 1-4 Notes Velocity & Displacement September 14

Mechanics Mechanics The study of the motion of objects The study of the motion of objects –Kinematics: the description of how objects move –Dynamics: forces and why objects move the way they do –Translational motion: objects moving without rotating Module 2-1

Reference Frames Reference Frames Any measurement of position, displacement, velocity or acceleration must be made with respect to a defined reference frame Any measurement of position, displacement, velocity or acceleration must be made with respect to a defined reference frame Module 2-1

Coordinate System Coordinate System Determine your reference frame, then set up a coordinate system Determine your reference frame, then set up a coordinate system Module 2-1 +x +y +x +y

Displacement Displacement = change in position Displacement is not always equal to the distance traveled Displacement = change in position Displacement is not always equal to the distance traveled Δx = x 2 – x 1 ΔxΔx

Displacement is positive: Right Up Displacement is negative: Left Down

Velocity A vector representing displacement occurring in a certain time interval A vector representing displacement occurring in a certain time interval Average velocity = change in position = displacement change in time time interval change in time time interval v avg = Δx = x 2 – x 1 Δ t t 2 – t 1 v avg = Δx = x 2 – x 1 Δ t t 2 – t 1

Speed Speed is the distance traveled in a certain time (direction is of no consequence) Speed is the distance traveled in a certain time (direction is of no consequence) If this motion took 10s, which would be greater here, velocity or speed? If this motion took 10s, which would be greater here, velocity or speed? ΔxΔx

Graphing Velocity Velocity can be determined by the slope of a line on a time vs. position graph Velocity can be determined by the slope of a line on a time vs. position graph Slope = rise/run = Δy/Δx Slope = rise/run = Δy/Δx

Instantaneous Velocity The velocity of the object at one instantaneous moment can be different from average velocity The velocity of the object at one instantaneous moment can be different from average velocity Slope of the tangent = velocity Slope of the tangent = velocity Instantaneous velocity and speed are the same value because distance = displacement when instantaneous Instantaneous velocity and speed are the same value because distance = displacement when instantaneous AP Physics equation sheet calls v speed AP Physics equation sheet calls v speed

Acceleration is the rate of change of velocity. Acceleration

Acceleration The change in velocity over time The change in velocity over time a = v 2 - v 1 Δt Δt

Acceleration is a vector, although in one-dimensional motion we only need the sign. Positive acceleration – acceleration in the direction of motion. Negative acceleration – acceleration opposite the direction of motion (decelerating) Exception to above: Acceleration is positive because direction of motion is negative

Practice Problems 2-1. The position of a runner as a function of time is plotted as moving along the x axis. During a 3.00s time interval, the runner’s position changes from x 1 =50.0m to x 2 =30.5m. What was the runner’s average velocity?

Practice Problems 2-2. How far can a cyclist travel in 2.5h along a straight road if her average speed is 18 km/h? 2-4. A car accelerates along a straight road from rest to 75km/h in 5.0s. What is the magnitude of the average acceleration?

Practice Problems 2-5. a) If the velocity of an object is zero, does it mean the acceleration is zero? Think of a situation to support your claim b) If the acceleration is zero, does it mean the velocity is zero? Think of a situation to support your claim.

Practice Problems 2-6. An automobile is moving to the right along a straight highway, which we choose to be the positive x axis, and the driver puts on the breaks. If the initial velocity is 15.0m/s and it takes 5.0s to slow down to 5.0m/s, what was the car’s average acceleration?

Physics Ch. 2 Motion in One Dimension Section 5-6 Notes Acceleration September 15 Don’t write the info in red font

Acceleration Acceleration is a measure of the rate of change in velocity Acceleration is a measure of the rate of change in velocity The change in velocity can be a change in the speed or in the direction The change in velocity can be a change in the speed or in the direction Ex. Units: m/s 2, mi/hr/s, km/hr/s

Graphing Acceleration The slope of a time vs. velocity graph equals the acceleration The slope of a time vs. velocity graph equals the acceleration

Uniform Acceleration When acceleration is constant When acceleration is constant Example: acceleration from gravity is a constant 9.8m/s/s Example: acceleration from gravity is a constant 9.8m/s/s

Displacement, again Displacement depends on acceleration, initial velocity and the time Displacement depends on acceleration, initial velocity and the time

Final Velocity Final velocity depends on initial velocity, acceleration and time Final velocity depends on initial velocity, acceleration and time -or-

Average Velocity (not on equation sheet)

Solving Problems 1. Read the whole problem and make sure you understand it. Then read it again. 2. Draw a diagram and choose coordinate axes. 3. Write down the givens and unknown (known quantities), and then the unknown ones that you need to find.

2-6 Solving Problems 4. Choose the appropriate equation based on your givens. Write down the equation(s). 5. Insert the givens (with units!!!) into equations 6. Solve algebraically keeping track of units and canceling when appropriate 7. Round answer using sig fig rules 8. Look at the result – is it reasonable? Does it agree with a rough estimate? 9. Check the units again.

An airplane accelerates along a 1.5km runway. It starts at rest and then reaches a velocity of 50.0m/s before taking off. What is its acceleration?

Practice Problems 2-7. You are designing an airport for small planes. One kind of plane that might use this airfield must reach a speed before take off of at least 27.8m/s (100km/h), and can accelerate at 2.00m/s 2. (a) If the runway is 150m long, can this airplane reach the proper take off speed? (b) If not, what minimum length must the runway have?

2-8. How long does it take a car to cross a 30.0m wide intersection after the light turns green, if it accelerates from rest at a constant 2.00m/s 2 ?

2-9. Estimate the minimum stopping distance for a car that is traveling 50 km/h and has an acceleration of -6.0m/s 2 once the brakes are applied. Take into account the driver’s reaction time of 0.50s during which time the car has an acceleration of zero.

Chapter 2 Homework #2 Questions: 7,8,11 Problems: 7,12,18,24,29,31, 39,40,41,42,45,46,49 General Problems: 60 Misconception Questions 1-9 Due Oct 1? Chapter 2 Test on Oct 2?

Physics Ch. 2 Motion in One Dimension Section 7 Notes Falling Objects September22

Near the surface of the Earth, all objects experience approximately the same acceleration due to gravity. This is one of the most common examples of motion with constant acceleration.

In the absence of air resistance, all objects fall with the same acceleration, although this may be hard to tell by testing in an environment where there is air resistance. Feather drop video Galileo’s Hypothesis

The acceleration due to gravity at the Earth’s surface is approximately 9.80 m/s 2.

Free Fall Objects in free fall undergo a constant acceleration from gravity Objects in free fall undergo a constant acceleration from gravity All the same kinematic equations apply, you can insert y in wherever there is an x

What goes up, must come down Objects thrown upwards undergo a constant negative acceleration from gravity Objects thrown upwards undergo a constant negative acceleration from gravity At the peak of their upward path, velocity is zero, then the object accelerates downward At the peak of their upward path, velocity is zero, then the object accelerates downward The up trip The up trip and down trip take the same amount of time

Practice Problems Suppose that a ball is dropped from a tower. How far will it have fallen after 1.00s, 2.00s and 3.00s? Assume y is positive downward. Neglect air resistance.

Practice Problems Suppose a ball is thrown downward with an initial velocity of 3.00m/s off the tower. (a) What would its position be after 1.00s and 2.00s? (b) What would its speed be after 1.00s and 2.00s? (c) Compare your answers in (b) to the speed of a ball that was dropped rather than thrown.

Practice Problems 2-12/13. A person throws a ball upward into the air with an initial velocity of 15.0m/s. Calculate (a) how high the ball goes and (b) how long the ball is in the air before it comes back to his hand. Neglect the throwing action, we only care about after the ball leaves the hand.

Practice Problems Explain the error in these two common misconceptions: (a) that acceleration and velocity are always in the same direction, and (b) that an object thrown upward has zero acceleration at the highest point.

Homework Due: Oct ? Test: Oct ?