Kinematics (Stuff moving) (stuff)
Start with vocabulary Position (x)– where it is (meters) Displacement ( x)– how far it moved, direction (+/-) is important (meters) Velocity – (v) how fast it moves, direction is important (+/-) (meters/second) –Instantaneous, right now! Slope of tangent Average velocity – change in position divided by change in time
Vocabulary, continued Acceleration (a) – rate of change in velocity –m/s 2 –Instantaneous, Slope of velocity time curve –Average, over time interval –Our equations apply only to constant acceleration –When acceleration changes, we break the problem into chunks of constant acceleration
The Equations! All you get on AP Equations Sheet Don’t forget these definitions!
Daddy
Mommy Notice no time in this one!
The area of a velocity “curve” is displacement! v t Avg velocity area
Tips for deciphering word problems …at rest, …from rest – not moving at beginning… v 0 = zero!..comes to rest… v f =zero …Travels 10 m in 10 sec… – x=10m, t=10 s …reaches a maximum height – velocity at h max = zero!
The Equations!
Kinematics Examples Drag race –Avg velocity given time and disp –Avg acceleration given final v and disp Motion Graphing –Aircraft Catapult Draw position and acceleration given velocity
Drag Race 1. A car travels meters in sec. What is its average velocity? 2. The same car reached m/s at the end of the first meters. What was its average acceleration?
Drag Race #1 Unknown: v avg =?? Given: x= meters in t= sec. Principle: Kinematics(where to look for eq’n) Equation: Picture: Simplify/Solve/Substitute
Drag Race #2 Unknown: a avg =?? Given: v f = m/s in x=201.17m Principle: Kinematics(where to look for eq’n) Equation: Picture: Simplify/Solve/Substitute zero
Aircraft catapult Navy aircraft are launched from the decks of aircraft carriers with a steam powered catapult. The graph shows the velocity of the aircraft as a function of time. Analyze the graph and draw corresponding position and acceleration graphs.
Aircraft Catapult(v) 50 v(m/s) time(s) 5
Aircraft Catapult(a) 20 a(m/s 2 ) time(s) 5
Aircraft Catapult(x) x(m) time(s)
Freefall Same kinematics equations… Just constant acceleration of a=g=9.8 m/s 2 toward earth. Do yourself a favor and call down negative.
1) A ball is dropped from 10 meters high. –A)How fast is it going when it hits the ground? –B) How long does it take to reach the ground? Freefall Example
2) A ball is given an upward velocity of 5.0 m/s, what is the maximum height it will reach? 3) How long does it take to reach this max height? Freefall Example
5) A ball is thrown upward with a velocity of 4.0 m/s. How fast is it going when it hits the ground, 10 meters below where it was thrown from? Freefall Example
Freefall Cases Downy –Dropping or “spiking” Uppy –Toss up Uppy – downy –Toss up off a ledge, object lands lower than the ledge Establish your coordinate system and be consistent with signs.
Wrap up Givens Unknowns P&P E –Time or none given S & S & S
More examples More example problems Try: v 0 =-3.0, a=5, t=4, x=? Try a “spike” (as in football player’s touchdown celebration) –x f =-5.0, x 0 =2.0, v 0 =-1.0, a=-9.8, t=?
The Equations! Don’t forget definitions
Drag Race #1 Unknown: v avg =?? Given: x= meters in t= sec. Principle: Kinematics(where to look for eq’n) Equation: Picture: Simplify/Solve/Substitute
Drag Race #2 Unknown: a avg =?? Given: v f = m/s in x=201.17m Principle: Kinematics(where to look for eq’n) Equation: Picture: Simplify/Solve/Substitute
Aircraft Catapult(v) 50 v(m/s) time(s) 5
Aircraft Catapult(a) 20 a(m/s 2 ) time(s) 5
Aircraft Catapult(x) x(m) time(s)
1) A ball is dropped from 10 meters high. –A)How fast is it going when it hits the ground? –B) How long does it take to reach the ground? Freefall Example
3) A ball is given an upward velocity of 5.0 m/s, what is the maximum height it will reach? 4) How long does it take to reach this max height? Freefall Example
5) A ball is thrown upward with a velocity of 4.0 m/s. How fast is it going when it hits the ground, 10 meters below where it was thrown from? Freefall Example