Update student slides & pdf notes for web PHYSICS Principles and Problems Update student slides & pdf notes for web Chapter 3: Accelerated Motion

Accelerated Motion BIG IDEA CHAPTER3 Accelerated Motion BIG IDEA Acceleration is the rate of change in an object’s velocity.

Nonuniform Motion Diagrams SECTION3.1 Acceleration Nonuniform Motion Diagrams An object in uniform motion moves along a straight line with an unchanging speed. Few objects move in uniform motion all the time.

Nonuniform Motion Diagrams (cont.) SECTION3.1 Acceleration Nonuniform Motion Diagrams (cont.) Objects more commonly move in nonuniform motion, in which velocity is changing. Nonuniform motion can be in a straight line: speeding up, applying brakes, falling objects. Nonuniform motion can be along a circular path: hammer throw, merry-go-round, driving around corner. Nonuniform motion can be the motion of thrown objects: baseball, football.

Nonuniform Motion Diagrams (cont.) SECTION3.1 Acceleration Nonuniform Motion Diagrams (cont.) You can feel a difference between uniform and nonuniform motion. When you move in nonuniform motion, you feel pushed or pulled. In contrast, when you are in uniform motion and your eyes are closed, you feel as though you are not moving at all.

Nonuniform Motion Diagrams (cont.) SECTION3.1 Acceleration Nonuniform Motion Diagrams (cont.) Consider the motion diagrams below showing the distance between successive positions. a. The person is motionless b. Equally spaced images show her moving at a constant speed. c. She is speeding up. d. She is slowing down.

Nonuniform Motion Diagrams (cont.) SECTION3.1 Acceleration Nonuniform Motion Diagrams (cont.) There are two major indicators of the change in velocity in this form of the motion diagram. The change in the spacing of the dots and the differences in the lengths of the velocity vectors indicate the changes in velocity.

Nonuniform Motion Diagrams (cont.) SECTION3.1 Acceleration Nonuniform Motion Diagrams (cont.) If an object speeds up, each subsequent velocity vector is longer. If the object slows down, each vector is shorter than the previous one.

Nonuniform Motion Diagrams (cont.) SECTION3.1 Acceleration Nonuniform Motion Diagrams (cont.) Both types of motion diagrams give an idea of how an object’s velocity is changing.

Nonuniform Motion Diagrams (cont.) SECTION3.1 Acceleration Nonuniform Motion Diagrams (cont.) For a motion diagram to give a full picture of an object’s movement, it should contain information about the object’s acceleration. The rate at which an object’s velocity changes is called the acceleration of the object. When the velocity of an object changes at a constant rate, it has a constant acceleration.

Direction of Acceleration SECTION3.1 Acceleration Direction of Acceleration The sign of the acceleration alone does not indicate whether the object is speeding up or slowing down. You need to know the direction of both the velocity and acceleration vectors in order to determine whether an object is speeding up or slowing down. When the acceleration of an object is in the same direction as its velocity, the object’s speed increases. When the acceleration of an object is in the opposite direction, the object’s speed decreases. Vector Scalar

Direction of Acceleration (cont.) SECTION3.1 Acceleration Direction of Acceleration (cont.)

Direction of Acceleration (cont.) SECTION3.1 Acceleration Direction of Acceleration (cont.) An object has a positive acceleration when the acceleration vector points in the positive direction and a negative acceleration when the acceleration vector points in the negative direction.

Acceleration Velocity-Time Graphs SECTION3.1 Acceleration Velocity-Time Graphs You can determine the acceleration from a velocity-time graph by calculating the slope of the graph. Click image to view the movie.

Acceleration Slope of a Velocity-Time Graph CHAPTER3 Acceleration Chapter Resources Slope of a Velocity-Time Graph The slope indicates the acceleration, measured in m/s2

Calculating Acceleration SECTION 3.1 Acceleration Calculating Acceleration Remember that acceleration of an object is the slope of that object’s velocity v. time graph. On a velocity v. time graph, slope equals:

Acceleration with Constant Speed SECTION 3.1 Acceleration Acceleration with Constant Speed Acceleration can occur when speed is constant. Consider a satellite orbiting around Earth at a constant speed. Even though speed is constant, direction is changing so the velocity is changing. If velocity is changing, then there is acceleration. We will cover this in more detail later in the course.

SECTION 3.1 Section Check Which of the following statements correctly defines acceleration? Acceleration is the rate of change of displacement of an object. Acceleration is the rate of change of velocity of an object. Acceleration is the amount of distance covered in unit time. Acceleration is the rate of change of speed of an object.

SECTION 3.1 Section Check What happens when the velocity vector and the acceleration vector of an object in motion are in the same direction? The acceleration of the object increases. The speed of the object increases. The object comes to rest. The speed of the object decreases.

SECTION 3.1 Section Check On the basis of the velocity-time graph of a car moving up a hill, as shown on the right, determine the acceleration of the car. 0.5 m/s2 -0.5 m/s2 2 m/s2 -2 m/s2

SECTION 3.1 Section Check Answer Reason: Average of an object is the slope of the velocity-time graph.

Motion with Constant Acceleration SECTION 3.2 Motion with Constant Acceleration MAIN IDEA For an object with constant acceleration, the relationships among position, velocity, acceleration and time can be described by graphs and equations.

Motion with Constant Acceleration SECTION 3.2 Motion with Constant Acceleration Position with Constant Acceleration The position data at different time intervals for a car with constant acceleration are shown in the table. The data from the table are graphed as shown on the next slide.

Motion with Constant Acceleration SECTION 3.2 Motion with Constant Acceleration Position with Constant Acceleration (cont.) The graph shows that the car’s motion is not uniform: the displacements for equal time intervals on the graph get larger and larger. The slope of a position-time graph of an object moving with a constant acceleration gets steeper as time goes on. For an object with constant acceleration, the shape of the position-time graph is a parabola.

Motion with Constant Acceleration SECTION 3.2 Motion with Constant Acceleration Position with Constant Acceleration (cont.) The slopes from the position time graph can be used to create a velocity-time graph as shown on the right.

Position vs. Time and Velocity vs. Time Note that the slopes shown in the position-time graph are the same as the velocities graphed in the velocity-time graph.

Motion with Constant Acceleration SECTION 3.2 Motion with Constant Acceleration Velocity with Constant Acceleration If an object’s acceleration during a time interval is known, then it can be used to determine how much the velocity changed during that time. The definition of acceleration: can be rewritten as follows:

Motion with Constant Acceleration SECTION 3.2 Motion with Constant Acceleration Velocity with Average Acceleration (cont.) To find final velocity, we add vi to both sides, giving us: The final velocity equals initial velocity plus the product of the acceleration and time interval. The equation can also be rewritten to find The time at which an object with constant acceleration has a given velocity. The initial velocity of an object when both the velocity and the time at which it occurred are given.

Motion with Constant Acceleration SECTION 3.2 Motion with Constant Acceleration Kinematic Equations Physicists and Mathematicians have worked together to come up with four equations (known as kinematic equations) that can be used in a variety of situations to describe and evaluate motion: xf = v∆t + xi vf = vi + a∆t xf = xi + vitf + ½atf2 vf2 = vi2 + 2a(xf - xi)

CHAPTER3 Accelerated Motion Chapter Assessment Which correctly describes the relationship between acceleration and velocity? A. Acceleration and velocity are the same thing. B. Acceleration is the rate of change in velocity. C. Acceleration is velocity with direction. D. Velocity is the rate of change in acceleration.

SECTION 3.2 Section Check A position-time graph of a bike moving with constant acceleration is shown below. Which statement is correct regarding the displacement of the bike? The displacement in equal time intervals is constant. The displacement in equal time intervals progressively increases. The displacement in equal time intervals progressively decreases. The displacement in equal time intervals first increases, then after reaching a particular point, it decreases.

CHAPTER3 Accelerated Motion Standardized Test Practice A ball rolls down a hill with a constant acceleration of 2.0 m/s2. The ball starts at rest and travels for 4.0 s. What is the ball’s velocity at the end of 4.0 s?

CHAPTER3 Accelerated Motion Standardized Test Practice A ball rolls down a hill with a constant acceleration of 2.0 m/s2. The ball starts at rest and travels for 4.0 s. How far did the ball travel?

CHAPTER3 Accelerated Motion Standardized Test Practice A bicyclist is riding at 5 m/s when she comes to a downhill portion of the road. She accelerates down the hill at a constant rate for 50 m, after which she is traveling at 10 m/s. What was her rate of acceleration?

Free Fall MAIN IDEA Essential Questions SECTION 3.3 Free Fall MAIN IDEA The acceleration of an object in free fall is due to gravity alone. Essential Questions What is free-fall acceleration? How do objects in free fall move?

Free Fall Galileo’s Discovery SECTION 3.3 Free Fall Galileo’s Discovery Free-fall is the motion of an object when gravity is the only significant force acting on it. After a lot of observation, Galileo concluded that, neglecting the effect of the air, all objects in free fall had the same acceleration. It didn’t matter what they were made of, how much they weighed, what height they were dropped from, or whether they were dropped or thrown. The acceleration of an object due only to the effect of gravity is known as free-fall acceleration.

Galileo’s Discovery (cont.) SECTION 3.3 Free Fall Galileo’s Discovery (cont.) The acceleration of falling objects, given a special symbol, g, is equal to 9.8 m/s2 downward for any object that is near the Earth’s surface. When analyzing free fall, whether you treat the acceleration as positive or negative depends on the coordinate system you choose.

Free-Fall Acceleration SECTION 3.3 Free Fall Free-Fall Acceleration Click image to view movie.

Free-Fall Acceleration (cont.) SECTION 3.3 Free Fall Free-Fall Acceleration (cont.) At the top of its flight, the ball’s velocity is 0 m/s. What would happen if its acceleration were also zero? Then, the ball’s velocity would not be changing and would remain at 0 m/s. If this were the case, the ball would not gain any downward velocity and would simply hover in the air at the top of its flight.

Free-Fall Acceleration (cont.) SECTION 3.3 Free Fall Free-Fall Acceleration (cont.) Because this is not the way objects tossed in the air behave on Earth, you know that the acceleration of an object at the top of its flight must not be zero. Further, because you know that the object will fall from that height, you know that the acceleration must be downward.

Free-Fall Acceleration (cont.) SECTION 3.3 Free Fall Free-Fall Acceleration (cont.) Amusement parks use the concept of free fall to design rides that give the riders the sensation of free fall. These types of rides usually consist of three parts: the ride to the top momentary suspension the plunge downward. When the cars are in free fall, the most massive rider and the least massive rider will have the same acceleration.

Free-Fall Acceleration (cont.) SECTION 3.3 Free Fall Free-Fall Acceleration (cont.)

Variations in Free Fall SECTION 3.3 Free Fall Variations in Free Fall The value of 9.8 m/s2 is only valid for objects in free-fall near the Earth. Later in the course we will study the factors that influence gravity, such as: Mass of the object. Ex. Earth or Moon Distance of the object in free-fall from the object responsible for the gravitational pull. Ex. Greater distance = less acceleration.

Section Check What is free fall? Answer: Free fall is the motion of the body when air resistance is negligible and the action can be considered due to gravity alone.

SECTION 3.3 Section Check A 50-kg bag and a 100-kg bag are dropped from a height of 50 m. Which of the following statements is true about their acceleration? (Neglect air resistance.) The 100-kg bag will fall with a greater acceleration. The 50-kg bag will fall with a greater acceleration. Both will fall at the same constant acceleration. Both will fall at the same acceleration, which changes equally as time progresses.

SECTION 3.3 Section Check Answer Reason: Any body falling freely toward Earth, falls with a same and constant acceleration of 9.8 m/s2. It doesn’t matter how much it weighs or what height it was dropped from.

CHAPTER3 Accelerated Motion Chapter Assessment A ball is thrown vertically upward. Which of the following statements is true when the ball is at its maximum height? A. The acceleration of the ball is zero. B. The velocity of the ball is at its maximum. C. The velocity of the ball is zero. D. The rate of change of velocity is zero.

CHAPTER3 Accelerated Motion Chapter Assessment Reason: When the ball reaches its maximum height, it stops, and starts falling down. So, when the ball is at its maximum height, the velocity of the ball is zero.

CHAPTER3 Accelerated Motion Chapter Assessment If a ball is dropped from a height of 20 m, what is the velocity of the ball after 1 s?

CHAPTER3 Accelerated Motion Chapter Assessment The acceleration due to gravity on the Moon is 6 times less than the gravity on Earth. If a ball on the Moon is dropped from a height of 20 m, what is the velocity of the ball after 1 s? A. - C. B. D.

CHAPTER3 Accelerated Motion Chapter Assessment Reason: The acceleration due to gravity on the Moon is m/s2. The rate of change of velocity of the ball on the Moon is m/s2. Hence, after 1 s, the ball will fall with a velocity of m/s.

SECTION 3.3 Section Check If a stone is thrown vertically upward with a velocity of 25 m/s, what will be the velocity of the stone after 1 second?

SECTION 3.3 Section Check Answer Reason: Since the ball is thrown upward, the velocity and acceleration are in opposite directions. Therefore the speed of the ball decreases. After 1 s, the ball’s velocity is reduced by 9.8 m/s (as acceleration due to gravity is 9.8 m/s2 downward), so it is now traveling at 25 m/s – 9.8 m/s = 15.2 m/s.

CHAPTER3 Accelerated Motion Standardized Test Practice A flowerpot falls off the balcony of a penthouse suite 85 m above the street. How long does it take to hit the ground?

CHAPTER3 Accelerated Motion Standardized Test Practice A rock climber’s shoe loosens a rock, and her climbing buddy at the bottom of the cliff notices that the rock takes 3.20 s to fall to the ground. How high up the cliff is the rock climber?