 # KINEMATICS KONICHEK. I. Position and distance I. Position and distance A. Position- The separation between an object and a reference point A. Position-

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KINEMATICS KONICHEK

I. Position and distance I. Position and distance A. Position- The separation between an object and a reference point A. Position- The separation between an object and a reference point 1. To locate something we must make some point a zero point- reference point 1. To locate something we must make some point a zero point- reference point 2. Measures both distance and direction 2. Measures both distance and direction B. Distance- needs no reference. B. Distance- needs no reference. 1. Measures the amount of separation 1. Measures the amount of separation 2. Measurement of only length 2. Measurement of only length C. Time- this is the interval between on reading of separation to the next reading of separation C. Time- this is the interval between on reading of 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 = D T /T T a.S A = D T /T T

E. Scalar and vector quantities. E. Scalar and vector quantities. 1. Scalar-measures only the magnitude or size 1. Scalar-measures only the magnitude or size a. Distance a. Distance b. Speed is a scalar- tells only how fast b. Speed is a scalar- tells only how fast 2. Vector- measures magnitude and direction 2. Vector- measures magnitude and direction

► II. Velocity ► A. Velocity- Speed in a given direction… ► 1.vector ► B. Constant velocity- ► 1. Motion remains constant at the same speed ►

C. Changing velocity- constant velocity and constant speed are not the same C. Changing velocity- constant velocity and constant speed are not the same 1. Constant speed can happen even if direction is changing 1. Constant speed can happen even if direction is changing 2. Constant velocity cannot occur- changing direction 2. Constant velocity cannot occur- changing direction D. Instantaneous velocity- this is the position of a moving object D. Instantaneous velocity- this is the position of a moving object 1. The position of the object changes with each new time taken. 1. The position of the object changes with each new time taken.

 E. Displacement-The change of position of an object.  1. Final distance - initial distance= ΔD  F. Time for moving objects  1. Final time - initial time=ΔT

D. Average velocity is the ratio of the change in displacement to a change in time D. Average velocity is the ratio of the change in displacement to a change in time 1. Va= d 2 -d 1 /t 2 -t 1 1. Va= d 2 -d 1 /t 2 -t 1 E. Constant velocity- Occurs when the average velocity is the same for all time intervals E. Constant velocity- Occurs when the average velocity is the same for all time intervals 1. Also called uniform velocity: 1. Also called uniform velocity: Δd/Δ t is constant. Δd/Δ t is constant. a. The equation then comes to v=d/t. This represents uniform velocity. a. The equation then comes to v=d/t. This represents uniform velocity.

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

III. POSITIVE AND NEGATIVE VELOCITIES. III. POSITIVE AND NEGATIVE VELOCITIES. A. Displacement can occur either positive or negative A. Displacement can occur either positive or negative 1. Positive moves to the right of the reference point 1. Positive moves to the right of the reference point 2. Negative- moves to the left of the reference point 2. Negative- moves to the left of 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 quantity I. Acceleration- vector quantity A. The rate which an objects velocity changes A. The rate which an objects velocity changes 1. Has to do with changing how fast is moving. 1. Has to do with changing how fast is moving. 2. Acceleration occurs when an object changes its velocity with respect to time. 2. Acceleration occurs when an object changes its velocity with respect to 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 CONSTANT ACCELERATION, THE DISTANCE OF TRAVEL IS DIRECTLY PROPORTIONAL TO THE SQUARE OF THE TIME TRVALED. C. LAW- FOR OBJECTS WITH A CONSTANT ACCELERATION, THE DISTANCE OF TRAVEL IS DIRECTLY PROPORTIONAL TO THE SQUARE OF THE TIME TRVALED. 1. Object travels twice the time it will go 4 times the distance. 1. Object travels twice the time it will go 4 times the distance. 2. travels 3 times the time, distance is 9 times father. 2. travels 3 times the time, distance is 9 times father.

II. Calculating acceleration. A. Ave acceleration= change in velocity/ time ave accel= V f - V i /t or ΔV/T 1. units- m/s 2 cm/s 2 ft/s 2 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 thumb C. Rule of thumb 1. If the object is slowing down, then the acceleration is in the opposite direction of motion. 1. If the object is slowing down, then the acceleration is in the opposite direction of motion. 2.can determine if the sign is positive or negative., right or left, up or down. 2.can determine if the sign is positive or negative., right or left, up or down. a. speeding up- accel is in the same direction as the velocity so it’s positive a. speeding up- accel is in the same direction as the velocity so it’s positive b. slowing down- acceleration is opposite that of the velocity, so it’s negative b. slowing down- acceleration is opposite that of the velocity, so it’s negative 3. direction- when the velocity is increasing in the direction of the speed- positive accel 3. direction- when the velocity is increasing in the direction of the speed- positive accel 4. When an object is slowing down in the direction of the velocity- negative accel 4. When an object is slowing down in the direction of the velocity- negative accel

► I. Acceleration-A change in velocity ► A. A change in speed or direction may occur ► 1. a= ΔV/ΔT ► a. change in velocity/ change in time ► 2. values may be positive or negative ► a. positive speeding up ► b. negative slowing down

II.Velocity of an object with constant accelerationII.Velocity of an object with constant acceleration A. Constant acceleration ( uniform) A. Constant acceleration ( uniform) 1. accel doesn’t change with time 1. accel doesn’t change with time a. V f = V i +at a. V f = V i +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(V f + V i )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(V f + V i )T-  1/2(V i +aT)+ Vi-  1/2((2V i +aT)t--  a. d= V i T+1/2at 2 a. V i T= displacement moving at a constant velocity b. 1/2at 2 = 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=1/2at 2

B. Velocity-time graph of uniform acceleration- the area under the curve equals the displacement. B. Velocity-time graph of uniform acceleration- the area under the curve equals the displacement. C. The curve for an accelerating position-time graph is parabolic C. The curve for an accelerating position-time graph is parabolic 1. When one value increases the other varies as the square of it. 1. When one value increases the other varies as the square of it. a. Y= X a. Y= X D. The slope of a position-time graph of an accelerating is a tangent point to the parabolic function D. The slope of a position-time graph of an accelerating is a tangent point to the parabolic function 1. Calculus people- second derivative function of the displacement formula 1. Calculus people- second derivative function of the displacement formula

V. Displacement when velocity and acceleration are known. V. Displacement when velocity and acceleration are known. A. combine the final velocity and displacement A. combine the final velocity and displacement 1. d=1/2(V f -V i )t and V f = V i +at, solve for t and substitute in the first equation 1. d=1/2(V f -V i )t and V f = V i +at, solve for t and substitute in the first equation a. final equation V 2 f = V 2 i +2ad a. final equation V 2 f = V 2 i +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. V f =V i +gt b. V 2 f = V 2 i + 2gd c. d= Vi+1/2 gt 2

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