KINEMATICS IN ONE DIMENSION Chapter 2

THINGS TO CONSIDER Are you moving at the moment? Are you at rest? Can you be moving and remain at rest at the same time? How do you know you are moving?

TYPES OF MOTION Translational Rotational Vibrational

POSITION RELATIVE TO… Object’s position is noted relative to other objects / systems of objects Frame of reference - a system for specifying the precise location of objects in space and time

MOVING = CHANGING LOCATION X i – initial coordinate (location) X f – final coordinate (location)

DISPLACEMENT / DISTANCE Distance: how much distance is covered by the object during motion. Magnitude only. Displacement: what is the change of location. BOTH magnitude and direction.

DISPLACEMENT VS. DISTANCE. A person walked 100 m south. a)What is the distance he walked? b)What is his displacement?

DISPLACEMENT VS. DISTANCE. A person walked 100 m south, turned around and walked 20 m back. a)What is the distance he walked? b)What is his displacement?

GIVE EXAMPLES Distance = displacement (in magnitude) Distance is greater than displacement Displacement is greater than distance Displacement = 0, distance > 0

Average speed is the distance traveled divided by the time required to cover the distance. SI units for speed: meters per second (m/s)

Example 1 Distance Run by a Jogger How far does a jogger run in 1.5 hours if his average speed is 2.22 m/s?

Average velocity is the displacement divided by the elapsed time.

Example 2 The World’s Fastest Jet-Engine Car Andy Green in the car ThrustSSC set a world record of m/s in To establish such a record, the driver makes two runs through the course, one in each direction, to nullify wind effects. From the data, determine the average velocity for each run.

VELOCITY GRAPH A straight line = const v

CONSTANT SPEED AND AVERAGE VELOCITY LAB Split into 4 groups Download the lab from physatwes or pick up a paper copy. Each student should turn in his / her own report The graph should be done on graph paper (not your laptop).

AVERAGE VS. INSTANTANEOUS

The notion of acceleration emerges when a change in velocity is combined with the time during which the change occurs.

DEFINITION OF AVERAGE ACCELERATION Calculate the average acceleration of a plane if, starting from rest, it reaches the speed of 260 km/h within 29 seconds.

GIVENUNITSEQUATIONS SUBSTITUTE / SOLVE Positive acceleration = speeding up

Calculate the average acceleration of a sports car if at t = 9s it is moving at the speed of 28 m/s and at t = 12 s it reaches the speed of 13 m/s. GIVENUNITSEQUATIONS SUBSTITUTE / SOLVE Negative acceleration = slowing down

ACCELERATION GRAPH

DOES “+A” ALWAYS MEAN SPEEDING UP?

DOES POSITIVE ACCELERATION ALWAYS MEAN “SPEEDING UP”? V(m/s) t (s)

MOTION WITH CONSTANT ACCELERATION v (m/s) t (s) vfvf vivi ∆t

A vehicle starts accelerating from rest at a rate of 2.5 m/s 2 for 4 seconds. What is the final velocity it reaches? What is the average velocity of the car during the 4 seconds? What is its displacement? GIVENUNITSEQUATIONSSUBSTITUTE / SOLVE

DISPLACEMENT (A=CONST)

A vehicle starts accelerating from rest at a rate of 2.5 m/s 2 for 4 seconds. What is the displacement that the car goes through in this time? Find it using two ways. GIVENUNITSEQUATIONSSUBSTITUTE / SOLVE

GIVENUNITSEQUATIONSSUBSTITUTE / SOLVE

FINAL VELOCITY (A=CONST)

GIVENUNITSEQUATIONSSUBSTITUTE / SOLVE

An Accelerating Spacecraft A spacecraft is traveling with a velocity of m/s. Suddenly the retrorockets are fired, and the spacecraft begins to slow down with an acceleration whose magnitude is 10.0 m/s 2. What is the velocity of the spacecraft when the displacement of the craft is +215 km, relative to the point where the retrorockets began firing?

GIVENUNITSEQUATIONSSUBSTITUTE / SOLVE

Free Fall Acceleration due to gravitation Galileo Galilei (1564 – 1642) In a system with no air resistance all objects fall with equal acceleration

In the absence of air resistance, it is found that all bodies at the same location above the Earth fall vertically with the same acceleration. If the distance of the fall is small compared to the radius of the Earth, then the acceleration remains essentially constant throughout the descent. This idealized motion is called free-fall and the acceleration of a freely falling body is called the acceleration due to gravity.

Galileo mathematically proved that distance traveled by an object falling down from rest is proportional to the square of the time period elapsed:

Example 10 A Falling Stone A stone is dropped from the top of a tall building. After 3.00s of free fall, what is the displacement y of the stone?

Example How High Does it Go? The referee tosses the coin up with an initial speed of 5.00m/s. In the absence if air resistance, how high does the coin go above its point of release? GIVENUNITSEQUATIONSSUBSTITUTE / SOLVE

Conceptual Example 15 Taking Advantage of Symmetry Does the pellet in part b strike the ground beneath the cliff with a smaller, greater, or the same speed as the pellet in part a?