Chapter 3 – Accelerated Motion. How would you describe the motion of the runner in each motion diagram? 3.1 Acceleration.

Chapter 3 – Accelerated Motion

How would you describe the motion of the runner in each motion diagram? 3.1 Acceleration

Change in velocity indicated by the change in spacing of the dots and the different lengths of the velocity vectors 3.1 Acceleration

acceleration – the rate at which an object’s velocity changes (units of m/s 2 ) when the velocity of an object changes at a constant rate, it has a constant acceleration

In which of these motion diagrams is the runner accelerating? 3.1 Acceleration

v-t graph for a cheetah Where was the cheetah at rest?

3.1 Acceleration v-t graph for a cheetah Why not at rest between 2 s and 3 s?

3.1 Acceleration What was happening during the first 2 s? v-t graph for a cheetah

3.1 Acceleration v-t graph for a cheetah What was the acceleration between 2 s and 3 s?

3.1 Acceleration v-t graph for a cheetah What was the acceleration between 4 s and 6 s?

3.1 Acceleration acceleration has both direction and magnitude, therefore, it is a vector quantity an object accelerates if its speed, direction, or both change a negative acceleration does not necessarily mean the object is slowing down, and a positive acceleration does not necessarily mean it is speeding up!!!

2.3 Position-Time Graphs Position-time graph for the ostrich Draw a velocity-time graph for this motion

3.1 Acceleration

Graph a negative acceleration, not slowing down Graph a positive acceleration that is slowing down (T or F) An object that is slowing down is accelerating

3.1 Acceleration this is a graph of a train moving Velocity in the positive direction is increasing (acceleration is +) Velocity in the positive direction is constant (acceleration is 0) Velocity in the positive direction is decreasing (acceleration is -)

3.1 Acceleration The slope of a v-t graph for an object is the object’s average acceleration - the change in velocity during some measurable time interval divided by that time interval. indicates an average

3.1 Acceleration Page 62 Figure 3-8 Remember!! The sign of the acceleration does not indicate whether the object is speeding up or slowing down.

3.1 Acceleration Describe the motion of a ball as it rolls up a ramp. The ball starts at 1.00 m/s, slows down for 2.00 s, stops for an instant, and then rolls back down at an increasing speed. The positive direction is chosen to be up the ramp, and the origin the place where the motion begins.

3.1 Acceleration Describe the motion of a ball as it rolls up a ramp. The ball starts at 1.00 m/s, slows down for 2.00 s, stops for an instant, and then rolls back down at an increasing speed. The positive direction is chosen to be up the ramp, and the origin the place where the motion begins. 1.At what point does the sign of the ball’s acceleration change? 2.Draw a velocity-time graph for the ball going up and down the ramp? 3.Draw an acceleration-time graph for the ball going up and down the ramp? 4.What is the magnitude of the ball’s acceleration? 5.When is the magnitude of the ball’s velocity at a minimum? 6.What is the sign of the ball’s acceleration as it rolls down the ramp?

3.1 Acceleration Describe the motion of a ball as it rolls up a slanted driveway. The ball starts at 2.50 m/s, slows down for 5.00 s, stops for an instant, and then rolls back down at an increasing speed. The positive direction is chosen to be up the driveway, and the origin the place where the motion begins. What is the sign of the ball’s acceleration as it rolls up the driveway? What is the magnitude of the ball’s acceleration as it rolls up the driveway?

3.1 Acceleration How can you determine velocity using a position time graph?

3.1 Acceleration What is the area under the velocity-time graph between t=2.0s and t=4.0 s?

3.1 Acceleration What is the area under the velocity-time graph between t=2.0s and t=4.0 s? 120 m What is the change in position on the position-time graph between t=2.0 s and t=4.0 s? How are these two answers related?

3.1 Acceleration How can you determine acceleration using the velocity-time graph?

3.1 Acceleration If the velocity were constant, what would the position-time graph look like? What would the acceleration-time graph look like?

3.1 Acceleration instantaneous acceleration – the change in velocity at an instant in time

3.1 Acceleration Which of the following statements correctly define acceleration? A. Acceleration is the rate of change of displacement of an object. B. Acceleration is the amount of distance covered in unit time. C. Acceleration is the rate of change of velocity of an object. D. Acceleration is the rate of change of speed of an object.

3.1 Acceleration What happens when the velocity vector (5 m/s) and the acceleration vector (2 m/s 2 ) of an object in motion are in same direction? A. The acceleration of the object increases. B. The speed of the object increases. C. The object comes to rest. D. The speed of the object decreases.

3.1 Acceleration On the basis of the velocity-time graph of a car moving up a hill, as shown on the right, determine the average acceleration of the car? A. -0.5 m/s 2 B. 0.5 m/s 2 C. 2 m/s 2 D. -2 m/s 2

3.1 Acceleration 1. What is the average acceleration of each car from 0.0 to 97.0 km/h (in m/s 2 )? 2. Which car can go from 0.0 to 97 km/h in the shortest time? Does this car have the highest or lowest acceleration? 3. For acceleration from 0.0 to 97 km/h, which direction is the acceleration vector pointing? 4. When a car is braking from 97 km/h to 0.0 km/h, is it positive or negative acceleration? 5. Which car is the safest?

3.1 Acceleration A hockey player glides along the ice at a constant speed of 1.25 m/s in the positive direction onto a rough section of ice, which slows him. If he stops in 5.0 s, what is the magnitude and direction of his acceleration?

3.2 Motion with Constant Acceleration If an object is accelerated for some time interval, we can rearrange our equation for average acceleration to determine its final velocity: Solving for:

3.2 Motion with Constant Acceleration Similarly, if an object is accelerated for some time interval, we can rearrange our equation for average acceleration to determine its final velocity: Solving for:

3.2 Motion with Constant Acceleration Kinematics Equation #1 Similarly, if an object is accelerated for some time interval, we can rearrange our equation for average acceleration to determine its final velocity: Solving for:

3.2 Motion with Constant Acceleration If an object is accelerated for some time interval, how does its position change? What is its displacement? so, With a constant acceleration,is ½ the sum of andbut,

3.2 Motion with Constant Acceleration If an object is accelerated for some time interval, how does its position change? What is its displacement? so, With a constant acceleration,is ½ the sum of and but, So,

3.2 Motion with Constant Acceleration Take and substitute into

3.2 Motion with Constant Acceleration

Kinematics Equation #2

3.2 Motion with Constant Acceleration Often, it is useful to relate position, velocity, and constant acceleration without including time. Recall,

3.2 Motion with Constant Acceleration Often, it is useful to relate position, velocity, and constant acceleration without including time. Recall, Solve for

3.2 Motion with Constant Acceleration Often, it is useful to relate position, velocity, and constant acceleration without including time. Recall, Solve for Recall,

3.2 Motion with Constant Acceleration Multiply by

3.2 Motion with Constant Acceleration Multiply by Kinematics Equation #3

3.2 Motion with Constant Acceleration Kinematics Equation #1 Kinematics Equation #2 Kinematics Equation #3

3.2 Motion with Constant Acceleration A position-time graph of a bike moving with constant acceleration is shown on the right. Which statement is correct regarding the displacement of the bike? A. The displacement in equal time intervals is constant. B. The displacement in equal time intervals progressively increases. C. The displacement in equal time intervals progressively decreases. D. The displacement in equal time intervals first increases, then after reaching a particular point it decreases.

3.2 Motion with Constant Acceleration Starting from rest, a ball rolls down an inclined plane at a constant acceleration of 2.00 m/s 2. a) What is the velocity after 8.5 s? b) How far does the ball roll in 10.0 s?

3.2 Motion with Constant Acceleration An engineer is to design a runway to accommodate airplanes that must gain a ground speed of 60.0 m/s before they can take off. If these planes are capable of being accelerated uniformly at the rate of 1.5 m/s 2 a) How long will it take a plane to achieve take off speed? b) What must be the minimum length of the runway?

3.2 Motion with Constant Acceleration A car traveling at 88 km/hr undergoes a constant acceleration of 8.0 m/s 2 as the brakes are applied a) How long does it take the car to come to a stop? b) How far does the car move after the brakes are applied?

3.2 Motion with Constant Acceleration A car rolls down a hill with a uniform acceleration of 2.0 m/s 2. At a certain point on the hill its velocity is 25.0 m/s a) What is the velocity 10.0 s later? b) How far has the car traveled during that 10.0 s?

3.3 Free Fall Free fall – the motion of a body when air resistance is negligible and the action can be considered due to gravity alone Galileo was the first to conclude that, neglecting the effect of air, all objects in free fall have the same acceleration.

3.3 Free Fall These skydivers are technically NOT in free fall because air resistance is acting upon them

3.3 Free Fall Acceleration due to gravity – the acceleration of an object in free fall that results from the influence of the Earth’s gravity  given the symbol, g  g = 9.80 m/s 2 In our study of free fall: Upwards is + Downwards is - Therefore, g = -9.80 m/s 2

3.3 Free Fall

Whether the egg is on the way up or the way down it is in free fall !!!!

3.3 Free Fall Like #36 1.An in-line skater first accelerates from 0.0 m/s to 8.5 m/s in 9.0 s, then continues at this constant speed for another 10.0 s. What ist he total distance traveled by the in-line skater? Like #93 2.How far does a plane fly in 20 s while it velocity is changing from 160 m/s to 70 m/s at a uniform rate of acceleration?

3.3 Free Fall

g = -9.80 m/s 2 v i = 4.9 m/s g = -1.62 m/s 2 v i = 16 m/s

3.3 Free Fall If a 50-kg bag and a 100-kg bag are dropped from a height of 50 m. Which of the following statement is true about their acceleration? (Neglect air resistance) A. 100-kg bag will fall with a greater acceleration. B. 50-kg bag will fall with a greater acceleration. C. Both will fall at the same and constant rate of acceleration. D. Both will fall at the same rate of acceleration, which changes equally as time goes.

3.3 Free Fall A stone is dropped from rest from the top of a tall building. After 3.00 s of free fall, what is the displacement of the stone? After 3.00 s of free fall, what is the velocity of the stone?

3.3 Free Fall At the coin toss of a football game, the ref tosses the coin straight up with an initial speed of 8.0 m/s. a) How long is the coin in the air? b) How high does it go?

3.3 Free Fall A ball is thrown vertically upward with a velocity of 11.5 m/s. a) To what height will it rise? b) How long to fall back to where it was released?

3.3 Free Fall Like #46 1.You decide to flip a coin to determine whether to do your physics or English homework first. The coin is flipped straight up. a.If the coin reaches a high point 0.53 m above where you released it, what was its initial speed? b.If you catch it at the same height as you released it, how much time did it spend in the air? Like #100 2.You throw a ball downward from a window at a speed of 4.0 m/s. How fast will it be moving when it hits the sidewalk 8.5 m below?

3.3 Free Fall Suppose you throw a ball straight up into the air. Describe the changes in the velocity of the ball. Describe the changes in the acceleration of the ball. The value of g on the Moon in one-sixth of its value on Earth. a)Would a ball that is dropped by an astronaut hit the surface of the Moon with a greater, equal, or lesser speed than that of a ball dropped from the same height to Earth? b)Would it take the ball more, less, or equal time to fall? Which has the greater acceleration: a car that increases its speed from 50 km/h to 60 km/h, or a bike that goes from 0 km/h to 10 km/h in the same time?

3.3 Free Fall Rock A is dropped from a cliff and Rock B is thrown upward from the same position, both at the same time. a)When they reach the ground at the bottom of the cliff, which rock has a greater velocity? b)Which has a greater acceleration? a)Which arrives to the ground first? When a ball is thrown vertically upward, it continues upward until it reaches a certain position, and then it falls downward. At the highest point, its velocity is instantaneously zero. Is the ball accelerating at the highest point?

3.3 Free Fall An object is thrown vertically into the air. Which of the following five graphs represents the velocity of the object as a function of the time? The positive direction is taken to be upward.

3.3 Free Fall For a truck moving at a constant velocity, the a) distance traveled during the second interval is greater than the distance traveled during the first interval b) directions during the first, second, and third intervals must be the same c) acceleration is increasing for each second d) velocity is increasing for each second

3.3 Free Fall Consider the following five graphs (note the axes carefully). Which of these represent(s) motion at constant speed?

3.2 Motion with Constant Acceleration What would the position-time graph for this object look like? What would the acceleration-time graph for this object look like?

3.2 Motion with Constant Acceleration How long will it take the object in Graph B to reach the velocity of the object in Graph A?

3.3 Free Fall Jason hits a volleyball so that it moves with an initial velocity of 6.0 m/s straight upward. If the volleyball starts from 2.0 m above the floor, how long will it be in the air before it strikes the floor? Assume that Jason is the last player to touch the ball before it hits the floor.

3.3 Free Fall A bungee jumper jumps from a bridge with a 75.0 m long bungee cord attached. He will free fall until the cord reaches its full length. How fast will he be going at the time the cord begins to stretch? The cord slows the jumper at the rate of 8.50 m/s 2 as it stretches out. What is the minimum height that the bridge must be to successfully complete the jump?

3.3 Free Fall 1. A baseball player hits a pop fly to a height of 40.8 m. After the bat strikes the ball, how much time will there be for a fielder to get into position to make the catch? 2. A stone is dropped from a balloon which is ascending at the rate of 5.80 m/s when the balloon is 350. m above the ground. What time is required for the stone to reach the ground?

3.2 Motion with Constant Acceleration The slope of the line on a v-t graph is the average acceleration of the object. What else can we see from the v-t graph?

3.2 Motion with Constant Acceleration Galileo’s Inclined Plane A board is raised to allow the ball to roll from rest to the.5 m position in the 1 st second The motion diagram represents the ball at 1 second intervals

3.2 Motion with Constant Acceleration Interval Start Time (s) End Time (s) Start Position (m) End Position (m) Distance Traveled (m) Average velocity (m/s) Inst. Velocity at start (m/s) Inst. Velocity at end (m/s) Ave. Acceleration (m/s 2 ) 10.01.00.00.5.50.01.0 2 2.00.52.01.5 1.02.01.0 32.03.02.04.52.5 2.03.01.0 43.04.04.58.03.5 3.04.01.0 54.05.08.012.54.5 4.05.01.0 Galileo’s Inclined Plane

3.2 Motion with Constant Acceleration What is the area under this line? The area under a v-t graph equal the object’s displacement! End Time (s) Inst. Velocity at end (m/s) End Position (m) 1.0 0.5 2.0 3.0 4.5 4.0 8.0 5.0 12.5

3.2 Motion with Constant Acceleration If an object has no initial velocity becomes The area under a v-t graph equal the object’s displacement!

3.2 Motion with Constant Acceleration What is the area under this line? The area under a v-t graph equal the object’s displacement!

3.2 Motion with Constant Acceleration The area under a v-t graph equal the object’s displacement! If an object has an initial velocity

Chapter 2 & Chapter 3 Vocabulary

A squirrel drops an acorn from a tree branch that is 8.00 m from the ground. Neglect air resistance. How long is the acorn in the air? What is the acorn’s velocity the instant before it hits the ground? A PATH train, starting from rest, pulls out of the Hoboken station with a constant acceleration of 1.55 m/s 2 for 17.5 seconds. It then rides under the Hudson River for 145.0 seconds at a constant speed. As it approaches 33rd Street station it slows down uniformly at 1.78 m/s 2 until coming to a stop. What total distance did the PATH train cover? How long (in minutes) did the trip take? What was the speed of the train right before it began slowing down?

3.2 Motion with Constant Acceleration A car is moving with an initial velocity of v i m/s. After reaching a highway, it moves with a constant acceleration of a m/s 2, what will be the velocity (v f ) of the car after traveling for t seconds? A. v f = v i + aΔt B. v f = v i + 2aΔt C. v f 2 = v i 2 + 2aΔt D. v f = v i – aΔt

Chapter 3 – Accelerated Motion. How would you describe the motion of the runner in each motion diagram? 3.1 Acceleration.

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Chapter 3 – Accelerated Motion. How would you describe the motion of the runner in each motion diagram? 3.1 Acceleration.

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Presentation on theme: "Chapter 3 – Accelerated Motion. How would you describe the motion of the runner in each motion diagram? 3.1 Acceleration."— Presentation transcript:

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