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Physics Unit 2: 1D Kinematics
Transcript of Physics Unit 2: 1D Kinematics
Position vs Time Graphs
Position vs Time Graphs (d vs t)
Velocity Vs Time & Acceleration vs Time graphs
V vs t & a vs t
Using the Velocity and Acceleration Equations
Acceleration Equations Examples.
Motion Diagrams, Displacement &Velocity
Create a motion diagram(Strobe, ticker tape) for an object traveling at the speed shown. Each tick mark on the axis is 1m, use a time interval of 1s.
Sections: 2.1-2.4 & 3.1-3.3
What is the magnitude of the runner's displacement between do and d1? What is the runner's time interval for this displacement?
Now go back and draw position vectors above each axis for the first second of motion and below the axis for the first 2s of motion. How could you use the position vector to find the displacement of the object between 1s and 2s?
Describe the motion of each object below as best you can. The number inside the dot it the time elapsed in seconds. The is the initial position.
Rank the objects based on the magnitude of their displacement between:
A) t=0s to t=2s
B) t=3s to t=4s
C) t=0s to t=4s
Is the runner shown below running at a constant speed? Explain
a. Find the Average speed and average velocity for each object below.
b. Find the largest instantaneous speed and velocity for each object above.
Motion Diagrams, Displacement and Distance
Ave. Speed & Velocity
As you have been studying motion diagrams the following terms have been discussed: Speed, Displacement, Velocity, Distance, Position, Time, Average Speed, Average Velocity, Instantaneous Speed, Instantaneous Velocity.
*Make two lists, on of all the scalars and one of all the vectors.
*So of the scalars are the magnitude of a vector quantity, draw an arrow linking a magnitude (scalar) to its corresponding vector.
Time and Speed
Speed & Velocity
Time interval is 1s
Time interval is 1.5s
Context Rich Problem
While walking on his nightly foot patrol, Chief Wiggum takes 1.5 km route from the Police Station Parking lot, thru the park, by the bronze statue of Jebediah Springfield, past the fountain and across the street to the Donut Shop and then back. Every there and back loop takes the Chief about 4.8 hours. The Statue is 0.5km away from the Police station, the fountain is 0.5km away from the Donut Shop and the park entrance is across a 0.25km wide street from the park entrance.
Last night on his way back from the Donut Shop, the Chief noticed a mustache and uni brow painted on the statue. Then he remembered that he and Bart left the Donut Shop at 8pm, and Bart was skate boarding with a speed of 0.25km/hr. He also passed Principle Skinner traveling 0.5km/hr on his bike and Nelson walking at a pace of 0.125 km/hr., both moving in the opposite direction as the Chief. Still a little confused about who to charge, Chief Wiggum checks the police station surveillance camera, and discovers that Nelson and Principal Skinner enter the park at 8 pm.
Who would you charge with the vandalism of the statue?
Ex. 6 - Position vs Time
A. Describe the motion of object 1 and 2.
Rank Each d vs t graph by ....
A. Largest to smallest instantaneous speed.
Ex. 9 Drawing position vs time graphs.
Mr. Branch is trying to make the fastest tumble buggy he can, so he opens up one of his blue tumble buggies and tinkers with the electronics. He has figured out a way to make his blue buggy use more electric energy every second. So his blue buggy will go faster but will run out of batteries quicker than the typical tumble buggy. One day he and his students decide to race tumble buggies, so Mr. Branch picks his blue tumble buggy and his students pick a red one. Mr. B is confident in his buggy so he gives the students a 1m head start.
At the start of the race the blue tumble is traveling twice as fast as the red one. After 6s the blue buggies batteries begin to run out and it starts to decrease speed after 10s the blue buggy has stopped all together, and the red buggy passes the blue buggy after 15s. Draw a position vs time graph for the first 20s of the race.
Object 1 -
Object 2 -
B. Calculate the average velocity for each.
C. Which object has the largest instantaneous velocity? What about instantaneous speed?
B. Largest to smallest instantaneous velocity.
C. Largest to smallest displacement.
D. Largest to smallest average velocity.
E. Largest to smallest average speed.
D. How would your answer to B change if you where looking for average speed instead of velocity?
A. Classify each object below as having increasing, decreasing or constant speed.
D vs t & Non-Constant velocity
A. A remote control car is 10m to the right of Mr. Branch, 1.25 minutes later the same car is 15m to the left of Mr. Branch. Calculate the speed and velocity of the car in m/s. Make a qualitative d vs t graph.
B. A tumble buggy has a velocity of -0.4m/s and is 30m from the origin when the timer is started. When the timer reads 50s, where is the tumble buggy?
C. While watching at a track meet, a student times his friend running the 100m. The student knows his friend can run with a speed of 10.2m/s, but when his friend finished the race the student's timer read 8.5s. Did the student start the timer when his friend was at the starting line?
B. Draw the instantaneous velocity vector for each object at each time interval. How do your vectors agree with your answer to part A?
Ex 10 Continued.
C. Draw acceleration vectors for each object.
D. Compare the direction between the acceleration vectors and velocity vectors for each object. What does this tell as about the objects speed?
EX 11. Acceleration Equations
A. A school bus starting from rest accelerates to a speed of 30m/s in 15 seconds, what was the bus's accelerations? Compare the direction of the acceleration vector to the final velocity vector.
B. A baseball traveling 45m/s comes to a complete stop in 0.83s when it strikes a catcher's mitt, what is the acceleration of the baseball? How does the direction of the baseball's velocity compare to the direction of the acceleration.
C. A mosquito is flying at a speed of 0.8m/s notices at bat is chasing it, so it accelerates at 0.5m/s^2 to try to get away. What is the mosquito's velocity after 3s of constant acceleration?
Equation for accelerating object on a D vs t graph.
Ex 15: Matching Graphs
Match each d vs t graph to its corresponding v vs t graph.
EX 13 d vs t and v vs t
A. Rank the objects largest to smallest, based on their acceleration (magnitude).
B. Use the d vs t graph to create V vs t graphs for each object.
C. Create a vs t graphs for each object.
Ex 12 - D vs t graphs
A. Describe the motion of each object who's d vs t graph is shown to the right. Include direction, velocity, acceleration, positive and negative.
B. Rank the objects based on their largest instantaneous speed.
1 - Blue
2 - Orange
3 - Green
4 - Red
5 - Purple
V vs T Graphs
Ex. 14: d and V vs t
Use V vs t graphs to find the final displacement and the distance traveled by each object.
t = 0s to t = 5s
t = 1s to t = 3s
t = 0 to t = 5s
t = 0 to t =2.5s
Ex 16: Story problems
A. Make a d vs t and v vs t graph for the following situation. Mr. Branch throws a ball upward, from 5m above the ground, with an initial upward velocity of 3m/s. Remember the acceleration due to gravity is -9.8m/s^2.
B. Find the displacement then make an a vs t graph and write a story that would match the graph below.
V vs t graphs
A. If the cannon launches the human cannon ball, from the ground, with an initial upward velocity of 30m/s how long will the human cannon ball be in the air for?
B. If the cannon is placed on a 5 m high platform how far off the ground is the human cannon ball when:
A. While surveying an near accident a police officer tries to give you a ticket for speeding because the skid marks you left on the pavement where 8.3m long, and the maximum braking acceleration of your car is 5.2m/s^2. If the speed limit was 15m/s, is the police officer justified in giving you a ticket?
B. You are designing a new highway on ramp and you are trying to figure out how long to make the ramp. You anticipate that car's entering the ramp will have a velocity of 5m/s and need to reach a velocity of 35m/s before leaving the ramp. If a reasonable acceleration for a car is 2.5m/s^2, how long should you make the on ramp?
A. A remote control car is traveling with velocity of 2.5 m/s to the right, when it experiences an acceleration of 0.4m/s^2 to the left for 3s. What is the remote control car's final velocity?
B. A student driver is attempting to talk their way out of a bad road test grade by explaining that the car was only accelerating at 10 m/s^2, after the light turned green, so we couldn't have been going too fast when I tried to turn 15s after going under the light. How fast was the car going when the student tried to turn?
Calculate the Average velocity and instantaneous Velocity for each object below.
Free Fall Examples:
Ex. 20. While standing on the roof of Kelloggsville high school, Mr. Branch drops a rock from the roof to the ground, and it takes 1.32s for the rock to hit the ground.
A. Draw a motion diagram for the rock.
B. How tall is the roof?
C. What is the rock's final velocity right before it hits the ground.
Ex 21. A PE student throws a dodge ball straight up with an initial velocity of 3m/s, from an initial height of 1.8m. What is the maximum height reached by the ball?