Kinematics 1D - Motion - Types of MotionTicker Tape DiagramMotion Graphs Slope = Slope = v d d v d d v v t t t t t t t t
Defining Position - Examples Scalar - Vector - Distance-Displacement : Δd = df– di Speed - Velocity- Examples A baseball player hits a homerun. It is 90ft to each base and the batter rounds the bases ending back at home plate… Q: What was the batters distance traveled and total displacement?
Vector Diagrams 1D Time = 10s for all Ex 1) Distance = Displacement = Speed = Velocity = Ex 2) Distance = Displacement = Speed = Velocity = Ex 3) Distance = Displacement = Speed = Velocity = Ex 4) Distance = Displacement = Speed = Velocity = Can distance and displacement be the same thing? If so, then when and what does that mean for speed and velocity under the same conditions?
Vector Diagrams 2D For each scenario, determine the resultants magnitude and direction… Distance vs Displacement Ex 1) Dist = Disp = Ex 2) Greater Distance: A B Greater Displacement: A B Q: If dA = 1500m and dB = 500m, how fast would A have to travel to reach peak at the same time as B? V = Pythagorean Theorem - Trigonometry -
Vector Components & Resultants… Displacement VectorsVelocity Vectors A dog runs 50m @ 40⁰ North of East.. A plane flies East at 100m/s while a wind blows North at 50m/s.. What are the x and y components? What is the resultant velocity of the plane? Graphically: Using a scale of 1cm = 10m Graphically: Using a scale of 1cm = 25m/s Analytically:Analytically: N E
Motion Graphs Displacement vs Time (d vs. t)Velocity vs. Time (v vs. t) Slope = Slope = Area = A- At rest B – Slow const velocity C – Fast const velocity D – Speeding Up E – Slowing down d v t t Acceleration vs Time (a vs. t) a a t t
d t v t
Kinematics Equations: A marble starts from rest and rolls down a 1.5m incline in ______s … Average Velocity: Q1: What is the average velocity of the marble? Q2: Was the marble moving at constant velocity? Q3: What was the final velocity of the marble? Acceleration: Q4: What was the acceleration of the marble? Distance Formula: Q5: Confirm that the marble rolled 1.5m. Final Velocity Formula: Q6: Confirm the final velocity.
Problem Solving Using Kinematics Equations A marble is given a push so that it rolls up an incline. The marble was given an initial velocity of 4m/s and rolls 2m in 1.2s. Assuming that ‘up the incline’ is considered the (+) direction. Determine the acceleration of the marble. Analyze – underline important and relevant information. (quantities, direction etc) Given/Find – list the given and find information to help determine which equation to use Equation– write down the equation necessary to solve the problem Algebra– use algebra (if necessary) to isolate the variable you are solving for Substitution – fill the given quantities into the equation WITH UNITS!!!!!! Answer – label your answer WITH UNITS and box in
Uniform Accelerated Motion A rocket ship in outer space sits motionless at rest. Then suddenly the engines ignite and the space ship begins to accelerate uniformly (at constant rate). After accelerating for 5s, the spaceship is traveling at 100m/s… Q1) At what rate does the space ship gain velocity? Q2) Draw a ticker tape diagram of the space ships motion. Q3) Complete the data chart.. Q4) Does the spaceship move the Same distance for each given second? Explain.. Time (s) Velocity(m/s) Displacement (m) Equation used Equation used 0 1 2 3 4 5 6 7 8
Directions:Fill in the values for the velocity for each second.. v0 = v3 = v4= v5 = v7 = v8 = v1 = v2 = v6 = t0 t1 t2 t3 t4 t5 t6 t7 t8 ∆d ∆d ∆d ∆d ∆d ∆d ∆d ∆d 0m 100m 200m 300m 400m 500m 600m 700m 800m Sketch the d-t and v-t graphs for the motion of the space ship d v t t Q) How far did the space ship go between the time interval 4 and 8 seconds?
Horizontal Kinematics- A car ride d t v t A car accelerates from rest at a constant rate of 2m/s2 for 10s in the positive direction… The car then slams on the breaks coming to a skidding stop in 10m… Q4) What was the deceleration of the car? Q5) How long did it take to come to a stop? Q6) What was the average velocity of the car during breaking? Q1) What is the final velocity after 10s? Q2) How far did the car go during this time? Q3) How long did it take to travel this distance? The car then cruises at a constant velocity for 1000m…
Motion of Falling Bodies: Aristotle vs Galileo http://library.thinkquest.org/11924/galileo.html Define Motion - Aristotle ( )Galileo ( ) Biography- Biography- Beliefs on MotionBeliefs on Motion
“Its easy estimate how fast an object falls for a given amount of time” Do Now: At what time is the acceleration the greatest? Explain in your own words what it means to accelerate at 9.81m/ss. In what document can you find this constant? From your homework, at what time does the distance an object falls and the velocity have the same numerical value? Estimate (using g=10)how fast an object is moving after falling for 15s? Now calculate the exact speed an object has after falling for 15s. How far will an object fall after 15s?
Free Fall – What can be asked and what to use…. I) How fast.. ( ) II) How far… ( ) Given Time No Time vi = 0 vi= 0 t = 7.5s d = 276m Given Time No Time vi = 0 vi= 0 t = 10s vf = 98.1m/s III) How much time.. ( ) IV) Find acceleration… ( ) Given DistanceGiven Speed vi = 0 vi= 0 d = 40m vf = 28m/s Given Given vi = 0 vi= 0 d = 7.29m vf = 4.86m/s t = 3s t = 3s
Free Fall – Objects thrown upwards…. A ball is shot upwards with an initial velocity of 39.24m/s… a) How long until it reaches its maximum height? b) What is the acceleration at its maximum height? c) What is the velocity at its maximum height? d) How high does the ball reach? Aka… e) What is velocity at 2s and 6s? f) What is the height of the object after 6.5s? g) If the ball reached only 50m high, what velocity was it shot with?
Vertical Kinematics- Free Fall Motion Neglecting air friction… A rock is dropped off of a cliff 100m tall.. Q1) How long until the rock hits the ground? Q2) How fast does it hit the ground? Q3) How fast would rock hit ground if it was thrown downward at 5m/s? a Dropped from rest, what velocity does an object have after falling… 1s… 2s… 3s… 4s… What would the motions graphs look like for a rock thrown upwards and landing back where it started? Note: d v t t
Free Fall – More complex situations During the shooting of a zombie apocalypse movie, a stunt is to be performed where a stranded character on a rooftop jumps and miraculously lands safely in a convertible rescue car that is moving. Q1: If the building is 15m high and the rescue car is a horizontal distance of 20m away from the landing point moving at a constant speed, how fast must the car be moving to catch the (stunt dummy)? Q2: If it takes .15s for the stunt dummy to come to rest from the moment it contacts the soft cushioned seat until its vertical velocity reaches zero, how many g’s does the stunt dummy experience? Why wouldn’t a ‘real’ human perform this stunt?
Free Fall – Extra Credit A man and his wife go for a ride in a hot air balloon. The balloon is rising into the sky at a constant speed of 5m/s. The husband decides to take an aerial photo of his children below when the balloon is 25m above the ground and accidentally drops his camera… Q: How long until the fathers camera hits the ground? Q: In an attempt to save his fathers camera, the son runs to catch the camera just before it hits the ground. If the son was a horizontal distance of 10m away from where the balloon lifted off, how fast does he have to run?