KINEMATICSKINEMATICS

KONICHEKKONICHEK

• I. Position and distanceI. Position and distance• A. Position- The separation between an object A. Position- The separation between an object

and a reference pointand a reference point• 1. To locate something we must make some 1. To locate something we must make some

point a zero point- reference pointpoint a zero point- reference point• 2. Measures both distance and direction2. Measures both distance and direction• B. Distance- needs no reference.B. Distance- needs no reference.• 1. Measures the amount of separation1. Measures the amount of separation• 2. Measurement of only length2. Measurement of only length• C. Time- this is the interval between on reading C. Time- this is the interval between on reading

of separation to the next reading of separationof separation to the next reading of separation

D. Speed( rate)= displacement/ time 1. Units of distance/ unit of time 2. Instantaneous speed- the speed of the object at the time of the observation. a. Looking at ones speedometer. 3. Average speed= total distance/total time

a.SAA= D= DTT/T/TTT

E. Scalar and vector quantities.E. Scalar and vector quantities. 1. Scalar-measures only the 1. Scalar-measures only the

magnitude or sizemagnitude or size a. Distancea. Distance b. Speed is a scalar- tells b. Speed is a scalar- tells

only how fastonly how fast 2. Vector- measures 2. Vector- measures

magnitude and directionmagnitude and direction

►II. VelocityII. Velocity► A. Velocity- Speed in a given A. Velocity- Speed in a given

direction…direction…► 1.vector1.vector► B. Constant velocity- B. Constant velocity- ► 1. Motion remains constant at the 1. Motion remains constant at the

same speedsame speed►

C. Changing velocity- constant velocity C. Changing velocity- constant velocity and constant speed are not the sameand constant speed are not the same

1. Constant speed can happen even 1. Constant speed can happen even if direction is changingif direction is changing

2. Constant velocity cannot occur- 2. Constant velocity cannot occur- changing directionchanging direction

D. Instantaneous velocity- this is the D. Instantaneous velocity- this is the

position of a moving objectposition of a moving object 1. The position of the object changes 1. The position of the object changes

with each new time taken.with each new time taken.

E. Displacement-The change of position E. Displacement-The change of position of an object.of an object.

1. Final distance - initial distance= 1. Final distance - initial distance= ΔΔDD F. Time for moving objectsF. Time for moving objects 1. Final time - initial time=1. Final time - initial time=ΔΔTT

D. Average velocity is the ratio of the change D. Average velocity is the ratio of the change in displacement to a change in timein displacement to a change in time

1. Va= d1. Va= d22-d-d11/t/t22-t-t11

E. Constant velocity- Occurs when the E. Constant velocity- Occurs when the average velocity is the same for all time average velocity is the same for all time intervalsintervals

1. Also called uniform velocity:1. Also called uniform velocity: ΔΔd/d/ΔΔ t is constant. t is constant. a. The equation then comes to a. The equation then comes to

v=d/t. This represents uniform velocity.v=d/t. This represents uniform velocity.

F. Position-time graphs.F. Position-time graphs. 1. Shows the position as a function of 1. Shows the position as a function of timetime 1. Time on X-axis, position on X- 1. Time on X-axis, position on X- axisaxis 2. Slope of a position- time graph.2. Slope of a position- time graph. a. The ratio of displacement to time a. The ratio of displacement to time is the same as rise over run of the line is the same as rise over run of the line (slope)(slope)

III. POSITIVE AND NEGATIVE III. POSITIVE AND NEGATIVE VELOCITIES.VELOCITIES.

A. Displacement can occur either A. Displacement can occur either positive or negativepositive or negative

1. Positive moves to the right 1. Positive moves to the right of the reference pointof the reference point

2. Negative- moves to the left 2. Negative- moves to the left of the reference pointof the reference point

• B. Time is always positive• C. Speed is the magnitude of the velocity• D. Velocity- includes speed and direction

of a moving object• 1. Can have a positive or negative

velocity• a. Depends which way the object

is moving relative to the frame of reference.

IV. Instantaneous velocity- The finding of the velocity for an instant.

A. Like looking at the speedometer of your car for just an instant.

B. It’s the slope of the tangent- If the graph shows an increasing velocity over various times the line is not a straight line, so the slope gives the instantaneous velocity.

1. First derivative of the displacement formula or limit ΔX/ΔT

V. Velocity-Time graph- very useful tool to describe motion.

A. time- x-axis, velocity on the y-axis B. The area under the line is equal to

the displacement of the object from its original position

1. When velocity is constant displacement increases linearly with time

a. Line is straight

VI Motion A. Speed- How fast an object is moving relative to a reference frame 1. ratio between distance and time ( scalar quantity-tells how

fast) a. speed=distance/time( S=d/t) b. m/s, Km/hr, Mi/hr 2. constant speed- when an equal distance is covered over an

equal time 3, Graphing speed a. time is on X axis b. distance on the Y axis c. the speed of the car can be calculated by calculating the

slope of the line( rise/ run).. Y=mx+b 1, steeper the slope faster it’s going

Graphing of Velocity

• Low velocity High velocity

VII. Relative velocity- this is the velocity as seen from a stationary frame of reference

A. A boat is traveling at 8m/s and a man on the boat is walking at 2m/s a man observing from the shore would see the man walking at 10m/s

I. Acceleration- vector quantityI. Acceleration- vector quantity A. The rate which an objects velocity A. The rate which an objects velocity

changeschanges 1. Has to do with changing how fast 1. Has to do with changing how fast

is moving.is moving. 2. Acceleration occurs when an 2. Acceleration occurs when an

object changes its velocity with respect to object changes its velocity with respect to time.time.

B. Constant velocity-When an object changes its velocity by the same amount each second.

1. Not the same as a constant velocity 2. The velocity is changing the same amount for every

increment of time a. constant velocity is not accelerating 3. Since accelerating objects are constantly changing

their velocities- The distance traveled per unit time is not a constant.

a. Free falling objects accelerate- objects in free fall will cover a longer distance over each period of time it has fallen

C. LAW- FOR OBJECTS WITH A C. LAW- FOR OBJECTS WITH A CONSTANT ACCELERATION, THE CONSTANT ACCELERATION, THE DISTANCE OF TRAVEL IS DIRECTLY DISTANCE OF TRAVEL IS DIRECTLY PROPORTIONAL TO THE SQUARE OF PROPORTIONAL TO THE SQUARE OF THE TIME TRVALED.THE TIME TRVALED.

1. 1. Object travels twice the time it will Object travels twice the time it will go 4 times the distance.go 4 times the distance.

2. travels 3 times the time, distance is 9 2. travels 3 times the time, distance is 9 times father.times father.

II. Calculating acceleration. A. Ave acceleration= change in

velocity/ time ave accel= Vf- Vi/t or ΔV/T

1. units- m/s2 cm/s2 ft/s2

B. Acceleration is a vector- has a direction 1. Depends if it is speeding up or

slowing down. 2. moving in a positive or negative

direction

C. Rule of thumbC. Rule of thumb 1. If the object is slowing down, then the 1. If the object is slowing down, then the

acceleration is in the opposite direction of motion.acceleration is in the opposite direction of motion. 2.can determine if the sign is positive or 2.can determine if the sign is positive or

negative., right or left, up or down.negative., right or left, up or down. a. speeding up- accel is in the same a. speeding up- accel is in the same

direction as the velocity so it’s positivedirection as the velocity so it’s positive b. slowing down- acceleration is opposite b. slowing down- acceleration is opposite

that of the velocity, so it’s negativethat of the velocity, so it’s negative 3. direction- when the velocity is increasing 3. direction- when the velocity is increasing

in the direction of the speed- positive accelin the direction of the speed- positive accel 4. When an object is slowing down in the 4. When an object is slowing down in the

direction of the velocity- negative acceldirection of the velocity- negative accel

► I. Acceleration-A change in velocityI. Acceleration-A change in velocity► A. A change in speed or direction may A. A change in speed or direction may

occuroccur► 1. a= 1. a= ΔΔV/V/ΔΔTT► a. change in velocity/ change in a. change in velocity/ change in

timetime► 2. values may be positive or negative2. values may be positive or negative► a. positive speeding upa. positive speeding up► b. negative slowing down b. negative slowing down

• II.Velocity of an object with II.Velocity of an object with constant accelerationconstant acceleration

• A. Constant acceleration A. Constant acceleration ( uniform)( uniform)

• 1. accel doesn’t change with 1. accel doesn’t change with timetime

• a. a. VVff= V= Vii +at +at

III. Displacement during constant acceleration

A. object is moving at a constant velocity 1. The area under a velocity time

graph B. d= ½(Vf+ Vi)t

IV Displacement when acceleration and time are known

A. combine the velocity with constant acceleration and the displacement during constant acceleration

1. d= ½(Vf+ Vi)T-1/2(Vi+aT)+ Vi-1/2((2Vi+aT)t-- a. d= ViT+1/2at2

a. ViT= displacement moving at a constant

velocity b. 1/2at2= displacement from rest to and moving

with uniform acceleration c. the sum of the 2 terms gives the displacement of

an object that starts with an initial velocity and accelerates uniformly.

2. starting from rest the equation comes down to d=1/2at2

• B. Velocity-time graph of uniform acceleration- the B. Velocity-time graph of uniform acceleration- the area under the curve equals the displacement.area under the curve equals the displacement.

• C. The curve for an accelerating position-time graph C. The curve for an accelerating position-time graph is parabolicis parabolic

• 1. When one value increases the other varies as 1. When one value increases the other varies as the square of it.the square of it.

• a. Y= Xa. Y= X• D. The slope of a position-time graph of an D. The slope of a position-time graph of an

accelerating is a tangent point to the parabolic accelerating is a tangent point to the parabolic functionfunction

• 1. Calculus people- second derivative 1. Calculus people- second derivative function of the displacement formulafunction of the displacement formula

• V. Displacement when velocity and V. Displacement when velocity and acceleration are known.acceleration are known.

• A. combine the final velocity and A. combine the final velocity and displacementdisplacement

• 1. d=1/2(V1. d=1/2(Vff-V-Vii)t and V)t and Vff= V= Vii+at, +at, solve for t and substitute in the first solve for t and substitute in the first equationequation

• a. final equation a. final equation VV22ff= V= V22

ii +2ad+2ad

VI acceleration due to gravity A. Galileo- first to show objects fall to the earth with the same

acceleration. 1. Rolled balls down an incline plane which rang bells at

intervals B. acceleration of gravity is represented by g 1. The acceleration is -9.8m/s2 a. vector- designate up as positive, and down as negative b. for each second something drops its speed increases

by 9.8m/s 2. equations for acceleration of gravity a. Vf=Vi +gt b. V2

f= V2i+ 2gd

c. d= Vi+1/2 gt2