2 Ch 02 Kinematics in One Dimension.pdf

(a) The velocity of the ball changes continuously. As it

(a) What happens to its velocity ?

(a) What is the height h of the building?

(b) Does its acceleration increase, decrease, or remain

(b) The acceleration of the ball remains constant while

(b) What is the total time of fall? h

(preferably the SI).

+215 km, relative to the point where the retrorockets began firing?

A ball is thrown upward . While the ball is in the air :

a hammer and a feather simultaneously from the same height. Both hit

A spacecraft is traveling with a velocity of v0 = +3250 m/s. Suddenly the retrorockets

A stone is dropped from the top of a tall building. After 3.00s of free fall, what

a. a smaller speed than,

a. No. The car is accelerating.

a. No. The car is slowing down.

absence of air resistance, would pellet B strike the ground with

Acceleration

acceleration of the coin, like

An experiment performed by astronaut David Scott (1971) who dropped

and the acceleration of a freely falling body

Andy Green in the car

Answer:

are fired, and the spacecraft begins to slow down with an acceleration whose magnitude

Average speed: is the distance divided by the elapsed time.

Average velocity - Figure 2.2

Average velocity: is the displacement divided by the elapsed time.

b. the same speed as, or

b. Yes. The car is slowing down and moving along the positive

b. Yes. The car is slowing down.

ball moves downward, its speed increases by 10

ball would stop at the peak, and remain there, which

beneath the cliff. Pellet B is fired straight downward at the same initial speed. In the

bodies at the same location above the Earth fall vertically

branch of physics known as

building. He falls freely from rest to the

By definition:

c. a greater speed than the pellet A.

c. No. The car is moving eastward.

c. No. The car is moving in the positive direction.

can be customized to describe the motion.

Chapter 1. Introduction and Mathematical Concepts.

Chapter 10. Simple Harmonic Motion and Elasticity.

Chapter 16. Waves and Sound.

Chapter 17. The Principle of Linear Superposition and

Chapter 2. Kinematics in One Dimension.

Chapter 28. Special Relativity.

Chapter 3. Kinematics in Two Dimensions.

Chapter 4. Forces and Newton’s Laws of Motion.

Chapter 5. Dynamics of Uniform Circular Motion.

Chapter 6. Work and Energy.

Chapter 7. Impulse and Momentum.

Chapter 8. Rotational Kinematics.

Chapter 9. Rotational Dynamics.

combined with the time during which the change occurs.

compared to the radius of the Earth, then the acceleration

Conceptual Example Taking Advantage of Symmetry

Conceptual Example: Acceleration Versus Velocity

Consider a car (which we treat as a particle) moving along

constant ?

Constant Acceleration (x0 = 0)

continue to convey the directions with a plus or minus sign.

d. Yes. The car is slowing down and moving along the negative

Definition of

determine the average

Determine the average acceleration of the plane.

direction of motion at each instant of time.

Does it make sense . 39

Does the car’s acceleration a necessarily have a negative value ? 31

downward and constant , whether the object is rising,

driver makes two runs

during each second of its motion. When it reaches

each direction, to nullify

EastWest

Enrich your background:

Equations of Kinematics for

Equations of Kinematics for Constant Acceleration

establish such a record, the

Example: A boat moving along a straight line

Example: Catapulting a Jet. Find its displacement.

Example: Distance Run by a Jogger

Example: The World’s

falling, or stopped at the top of its “trajectory”. Objects

Fastest Jet-Engine Car

Feather and Hammer Drop on the Moon: http://www.youtube.com/watch?v=5C5_dOEyAfk

Fig. A Fig. B

Find its displacement after 8.0 seconds.

free fall acceleration

from rest are all falling freely once they are released.

Graphical Analysis of Velocity and Acceleration

Graphical Analysis of Velocity and Acceleration

Graphical Analysis of Velocity and Acceleration

Graphical Analysis of Velocity and Acceleration

gravity only, accelerate toward the earth with constant acceleration of

ground a distance of h. It takes him 1.0 s

ground at the foot of the cliff. Ignoring air

hkm

hkm0hkm260 +=

How far does a jogger run in 1.5 hours (5400 s) if his average speed is

How to Solve?

How to Solve?

https://www.youtube.com/watch?v=89NdAq8rQYQ https://www.youtube.com/watch?v=41a3DR0sZ-c

If a car is slowing down, can its acceleration be positive?

If a car is travelling eastward, can its acceleration be westward?

in which velocity changes are pointing.

indices i and f refer to the initial and final values. 3

initially with speed 6.0 m/s with acceleration 2.0 m/s 2.

Interference Phenomena.

is 10.0 m/s 2 . What is the velocity of the spacecraft when the displacement of the craft is

is called the acceleration due to gravity.

is not the case .

is the displacement y of the stone?

is the free-fall acceleration, g ≅ 10 m/s 2 .

It is customary to dispense with the use of boldface

it is in the air, from the instant it leaves the hand until

its point of release?

kinematic equations.)

leaning tower of Pisa and found that g is nearly the same. Although

Let the object be at the origin when the clock starts i.e.:

magnitude g ≅ 9.8 m/s2.

Motion with Constant Acceleration

Newton in his development of the laws of motion. 46

Note: If the acceleration were zero at the peak when

ntDisplaceme

ntdisplaceme=−=∆ oxxx 

of a fog-shrouded cliff. To find the height of

of the most precisely tested laws of nature.

One of the kinematic equations:

Page

part to another?

path, the coin momentarily has zero velocity. On the

Pellet A is fired straight upward from a gun at the edge of a cliff. The initial speed of

Poll 1:

Poll 2:

POLL(3) 56

positioninitial=ox

proportional to the square of the time taken (consistent with one of the

Puzzling question: A car traveling along a straight road and is decelerating.

Q: In the absence of air

remains essentially constant throughout the descent.

resistance, does the

resistance, how high does the coin go above

resistance, how high is the cliff if the speed of

rolling balls down inclined planes. He found that the displacement is

Speed and Velocity

speed of 5.00 m/s. In the absence of air

speedAverage =

speedAverage =

speeds near the surface of the earth neglecting the air friction.

Spider-man steps from the top of a tall

Suppose you are climbing in the High Sierra

symbols overdrawn with arrows for the displacement,

the ground at the same time.)

the instant before it strikes the ground. Its magnitude

The instantaneous velocity indicates how fast the car moves and the

the moon, where there is no air to retard the motion ( gmoon ≅ gearth .)

The notion of acceleration emerges when a change in velocity is

the peak of its motion, its speed becomes zero. As the

the pellet is 30 m/s. It goes up and then falls back down, eventually hitting the ground

The referee tosses the coin up with an initial

the velocity were zero, this would say that there

the velocity, change from one

the x axis from a point P to a point Q , as shown, where the

There are three parts to the motion of the coin. On the

there is some doubt that this particular experiment was carried out, it is

This choice makes the acceleration = − g . 52

this cliff, you drop a rock from the top and,

This idealized motion is called free-fall

through the course, one in

thrown upward or downward and those released

ThrustSSC set a world record

timeElapsedspeedAverageDistance

to fall the last h/4 distance of his fall.

Together, kinematics and dynamics form the

travels upward, its speed decreases by 10 m/s

upward and has decreasing magnitude. At the top of its

using the letters x , xo ,v ,vo ,a or t. Use consistent unit system

Usually, it is important:

Wagih Ghobriel

way down, the coin has downward-pointing velocity

way up, the coin has a vector velocity that is directed

We can derive one kinematic equation from another one:

well established that Galileo did perform many systematic experiments on

when you suddenly find yourself at the edge

Which is another kinematic equations

wind effects. From the data,

with an increasing magnitude.

with the same acceleration. If the distance of the fall is small

would be no change in velocity thereafter, so the

 All objects near the surface of the earth moving under the influence of

 Draw a coordinate axis on your picture and assign the origin x=0.

 Draw a picture of the situation described.

 Finally , think about your answer. Check for the algebra errors.

 Free-fall is closely approximated for objects falling near the surface of

 Galileo’s achievements in the science of mechanics paved the way for

 Galileo’s model is an accurate description of objects traveling at low

 Identify a special condition regarding the unknown quantity.

 Identify the letter that corresponds to the unknown quantity

 In the absence of air resistance, it is found that all

 Our four equations for constant acceleration

 Pick the appropriate one of the four kinematic equations.

 Solve the equations algebraically for the unknown.

 The universality of the rate of free fall is one

 There is a legend that Galileo dropped rocks with different sizes from the

 Translate the words (prose) describing the problem into equalities

 Variation of the acceleration due to gravity or

The acceleration of an object near the earth’s surface is

 If the velocity and acceleration have , the object is

 If the velocity and acceleration have the , the object is

 In either case, the sign of the acceleration indicates the direction