Physics11–’Kinematics0’Scalarvs.Vector...Runnata Gass is driving through town at 25.0 m/s and...
Transcript of Physics11–’Kinematics0’Scalarvs.Vector...Runnata Gass is driving through town at 25.0 m/s and...
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Physics 11 – Kinematics -‐ Scalar vs. Vector
-2 -1 0 1 2 3 4 5 6 7 8
A B
Scalar quantities have only a magnitude (amount).
Vector quantities have a magnitude and a direction. We represent them as arrows.
Distance (d): the separation between two points. Is distance a scalar or a vector? _____________
Displacement (Δd): A measure of the change in position. Is displacement a scalar or a vector? ______________
Δd = final position – initial position. The sign of the value for indicates the direction.
a) what is the distance of Car A from Car B? ___________ (scalar / vector)
b) what is the distance of Car B from Car A? ___________ (scalar / vector)
c) what is the position of Car A? ____________ (scalar / vector) of Car B? ____________(scalar / vector)
d) what is the displacement of Car A measured from Car B? ________(s/v)
e) what is the displacement of Car B measured from Car A? ________(s/v)
Ex: A student walks 5 m east and then 3 m west.
a) What is the distance (scalar) travelled?
b) What is the student’s displacement (vector)?
NOTE: When adding Vectors…
Ex: A polar bear meanders 275 m east and then turns around and ambles 425 m west.
a) What was the distance travelled by the bear?
b) What was the bear’s displacement?
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1 2 3
4 5 6
Describe the following angles Ex: A little girl takes her dog for a walk around a city block as shown.
a) What is the distance travelled?
b) What is her final displacement?
c) What was her displacement at C?
d) What was her displacement at B?
Add each of the following vectors and find the total resultant.
1) 15 m East and 25 m North
2) 220.0 m North and 80.0 m West
3) 2.2 m South and 1.8 m North
4) 150 m East and 180 m South
5) 45.0 m South and 30.0 m East and 15.0 m North
θ
θ θ
θ
θ
θ
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Physics 11 – Kinematics -‐ Speed vs. Velocity
Speed (v):
• Speed is a
Velocity (v):
• Velocity is a
Where Δ means
Ex: A student travels 11 m north and then turns around and travels 25 m south. If the total time of travel is 12 s, find:
a) The student’s average speed.
b) The student’s average velocity.
1) How long does it take a car traveling at 45 km/h to travel 100.0 m?
2) How far does a skateboarder travel in 22 s if his average velocity is 12.0 m/s?
3) A shopping cart moves from a point 3.0 m West of a flagpole to a point 18.0 m East of the flagpole in 2.5 s. Find its average velocity.
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Average Velocity and Speed
1. A high school bus travels 240 km in 6.0 h. What is its average speed for the trip? (in km/h)
2. A spider travels across a driveway 3.6 m wide with a speed of 14 cm/s. How long will it take to cross the driveway?
3. Jay Umpshot, one of the many stars of the local basketball team, steals the ball and runs the length of the court in 8.5 seconds at a speed of 5.0 m/s. How long is the court?
4. If a car is traveling at 25 m/s, how far does it travel in 1.0 hour?
5. A caterpillar travels across the length of a 2.00 m porch in 6.5 minutes. What is the average velocity of the caterpillar in m/s?
6. A motorist traveling on a straight stretch of open highway sets his cruise control at 90.0 km/h. How far will he travel in 15 minutes?
7. A motorcycle travels 90.0 km/h. How many seconds will it take the motorcycle to cover 2.10 x 103 m?
8. A hiker is at the bottom of a canyon facing the canyon wall closest to her. She is 280.5 m from the wall and the sound of her voice travels at 340.0 m/s at that location. How long after she shouts will she hear her echo.
9. A woman makes a trip to a nearby shopping mall that is located 40.0 km from her home. On the trip to the mall she averages 80.0 km/h but gets a speeding ticket upon her arrival. On the return trip she averages just 40.0 km/h. What was her average speed for the entire trip?
10. A cross-‐country rally car driver sets out on a 100.0 km race. At the halfway marker (50.0 km), her pit crew radios that she has averaged only 80.0 km/h. How fast must she drive over the remaining distance in order to average 100.0 km/h for the entire race?
11. A supersonic jet travels once around the earth at an average speed of 1.6 x 103 km/h. Its orbital radius is 6.5 x 103 km. How many hours does the trip take?
1) 4.0x101 km/h 2) 26 s 3) 43 m 4) 9.0x104 m 5) 5.1x10-‐3 m/s 6) 23 km 7) 84.0 s 8) 1.650 s
9) 53.3 km/h 10) 133 km/h 11) 26 h
A motorist travels 160 km North at 80.0 km/h and then 110 km South at 100.0 km/h. What is the average speed and average velocity of the motorist for this trip?
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Physics 11 – Kinematics – Uniform Accelerated Motion
Acceleration:
Ø Acceleration is a______________.
Anytime an object’s...
1) A sprinter starts from rest and reaches a speed of 12 m/s in 4.25 s. Find his acceleration.
2) A car starts from rest and accelerates at 15 m/s2 for 3.0 s. What is its top speed?
3) If a snowboarder is traveling at 8.0 m/s how long will it take her to reach 36.0 m/s if she can accelerate at a rate of 3.5 m/s2
The acceleration of an object can be found with:
Where:
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Acceleration Practice
1) John is running with a jet pack from rest and accelerates up to 90.0 m/s in 6.0 s. What is John’s acceleration? (15 m/s2)
2) Mackie is riding a high-‐powered train that accelerates 40.0 m/s2 for 3.0 min. If the train starts at rest, what is the train’s final velocity? (7.2 x 103 m/s)
3) If Strawberry Shortcake accelerates in her Muffin Mobile at 10.0 m/s2, starting from rest, and her finishing speed is 112 m/s, how long did her trip take? ( 11.2 s )
4) A bird is buzzing around at 24 m/s. The bird decides to accelerate at 2.0 m/s2 for 8.0 s. What is the bird’s final velocity? (4.0 x 101 m/s)
5) A bicycle travels at 18 m/s then comes to a stop. If this took 4.0 s, what was the bike’s acceleration? ( -‐4.5 m/s2 )
6) Suzie Lvkestaski has reached the end of the ski slope and abruptly slows from 29.0 m/s to 1.80 m/s in 1.45 seconds. Determine Suzie's acceleration rate she moved during this braking period. ( -‐ 18.8 m/s2 )
7) A dragster accelerates from rest to 200.0 km/h in 2.0 s. What is its acceleration (28 m/s2)
8) During the annual shuffleboard competition, Renee gives her puck an initial speed of 9.32 m/s. Once leaving her stick, the puck slows down at a rate of -‐4.06 m/s2. Determine the time it takes the puck to slow to a stop. (2.30 s)
9) A rock rolls down a hill with an acceleration of 7.8 m/s2, reaching 25 m/s in 2.2 s. What was its initial velocity? (7.8 m/s)
Motion Velocity Acceleration A car sitting at a stop light hits the gas
From rest you back out of your driveway
A plane lands and comes to a stop
You drop a rock off a cliff
You throw a rock straight up
Anytime an object’s velocity is changing, it is accelerating.
Ø An increase in velocity is
Ø A decrease in velocity is
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Physics 11 – Kinematics – Graphing Motion
Sketch each of the following situations:
For d vs. t graphs:
� Slope =
For v vs. t graph:
� Slope =
• Area under graph =
1) A hockey player skates at a constant speed from blue line to blue line.
d (m)
t (s)
v (m/s)
t (s)
2) A football is kicked straight up and then falls back down.
d (m) t (s)
v (m/s)
t (s)
3) A swimmer swims the length of a pool at a constant speed, quickly turns around and swims back.
d (m) t (s)
v (m/s) t (s)
4) A person speeds up to a maximum speed then travels for a while at that speed
d (m) t (s)
v (m/s) t (s)
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1. Runnata Gass is driving through town at 25.0 m/s and begins to accelerate at a constant rate of –1.00 m/s2. Eventually Runnata comes to a complete stop. Represent Runnata's accelerated motion by sketching a velocity-time graph. Use the velocity-time graph to determine the distance traveled while slowing.
2. Otto Emissions is driving his car at 25.0 m/s. Otto accelerates at 2.0 m/s2 for 5.0 seconds. Otto then maintains this constant velocity for 10.0 more seconds. Represent the 15 seconds of Otto Emission's motion by sketching a velocity-time graph. Use the graph to determine the distance Otto traveled during the entire 15 seconds.
3. Chuck Wagon travels with a constant velocity of 0.50 m/s for 10.0 s. Chuck then accelerates at –0.25 m/s2 for 2.0
seconds. Sketch a velocity-time graph for Chuck Wagon's motion. Use the velocity-time graph to determine the total distance traveled by Chuck Wagon during the 12.0 seconds of motion.
4. Earl E. Bird travels at 30.0 m/s for 10.0 seconds. He then accelerates at 3.00 m/s2 for 5.00 seconds. Construct a
velocity-time graph for Earl E. Bird's motion. Use the plot to determine the total distance traveled.
Imagine a car at a stop light. When the light turns green it accelerates forward at a constant rate.
Sketch d vs. t, v vs. t and a vs. t graphs of its motion.
Tex Ting is traveling down the interstate at 45.0 m/s when ahead he sees an accident in the middle of the road. It takes Tex 1.5 s to recognise the danger and slam on the brakes. He slows down at a rate of –15.0 m/s2. Construct a velocity-‐time graph for Tex Ting’s motion to determine the distance he would travel prior to reaching a complete stop.
1) 313 m 2) 5.0 x 102 m 3) 5.5 m 4) 488 m
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Physics 11 – Kinematics – Interpreting Motion Graphs
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Physics 11 – Kinematics – The Kinematics Equations of Motion
If an object is accelerating then the formula:
Gives us only the _______ ________
We can also find average velocity using:
1) Ex: A squad car traveling at 7.0 m/s East speeds up to 22.0 m/s East in 1.7 s. What is its acceleration?
In order to solve problems with uniform acceleration we need to use 3 formulae. These 3 formulae use the variables:
vf = vo = a = Δd = ` t =
3) Ex: A car accelerates from 15.0 km/h at 2.00 m/s2. How far has it traveled when it reaches 30.0 km/h?
2) Ex: A sprinter starts from rest and accelerates uniformly. He travels 100.0 m south in 9.69 s, what was his average acceleration?
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Kinematic Equations
1. A ball rolling down a ramp was displaced 19.6 m while uniformly accelerating from rest. If the final velocity was 5.00 m/s. what was the rate of acceleration?
2. If a bullet leaves the muzzle of a rifle at 600.0 m/s, and the barrel is 0.90 m long, what was the acceleration of the bullet while in the barrel?
3. The Jamaican bobsled team hit the brakes on their sled so that it slows at a uniform rate of 0.43 m/s². How long does it take to stop if it travels 85 m before coming to rest?
4. A car starts from rest and accelerates uniformly to reach a speed of 21 m/s in 7.0 s. What was the speed of the object after 2.0 seconds?
5. A bike rider accelerates uniformly at 2.0 m/s² for 10.0 s. If the rider starts from rest, calculate the distance traveled in the fourth second. (i.e. between t = 3 s and t = 4 s).
6. CHALLENGE: A driver of a car going 90.0 km/h suddenly sees the lights of a barrier 40.0 m ahead. It takes the driver 0.75 s before he applies the brakes (this is known as reaction time). Once he does begin to brake, he slows at a rate of 10.0 m/s².
a) Does he hit the barrier?
b) SUPER-‐CHALLENGE: What would be the maximum speed at which the car could travel and NOT hit the barrier 40.0 m ahead?
Ex 1: A dragster initially at rest at a stop light hits the gas and reaches 100.0 km/h in 3.2 s.?
a. What is its acceleration?
b. How far does he travel in this time?
Ex 2: A ball is rolled ramp a hill at 3.6 m/s. After 4.0 s it is travelling at 8.2 m/s. How far did it roll?
1) 0.638 m/s2 2) 2.0 x 105 m/s2 3) 2.0 x 101 s 4) 6.0 m/s 5) 7 m 6a) YES!! 6b) 78 km/h
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Physics 11 – Kinematics – Acceleration Due to Gravity
• In the absence of air friction…
•Near Earth’s surface the acceleration is
Example: A student drops their homework down a wishing well. After 2.4 s it hits the water at the bottom. How deep is the well?
Example: A football is kicked straight up in the air at 15 m/s. a) How high does it go?
b) What is its total hangtime?
Example: A student stands on the edge of a 45.0 m high cliff. They throw their physics homework straight up in the air at 12.0 m/s. a. How long does it take to come back down to the same height as the student?
b. If it falls all the way to the bottom of the cliff, how fast is it traveling when it hits the ground?
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1) Mario jumps straight upwards with a velocity of 14.0 m/s. What is his displacement of after 1.80 s? (9.32 m)
2) Luigi jumps straight upwards at 15.0 m/s. How high is he when he is travelling at:
a) 8.0 m/s upwards? (8.2 m) b) 8.0 m/s downwards? (8.2 m)
3) Sick of his guff, Optimus Prime decides to throw Megatron down off the top of a building at 5.0 m/s. Megatron hits the ground traveling at 32.0 m/s.
a) How long does it take to hit the ground?(2.8 s)
b) How far does he fall?(- 51 m)
4) While strolling along on Planet X an astronaut decides to throw a hammer and a feather upwards at 5.0 m/s. They both return to the point of release in 3.0 s. What is the acceleration due to gravity on Planet X? (-3.3 m/s2)
5) Princess Toadstool stands on the edge of a 30.0 m high cliff. She throws Bowser upwards at 20.0 m/s. If Bowser falls all the way to the bottom of the cliff, find:
a) his velocity when he hits the ground. (-31.4 m/s)
b) the time it takes to hit the ground. (5.24 s)
Acceleration Due to Gravity
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Physics 11 – Kinematics – Horizontal Projectile Motion
Remember that the x and y-‐components are _______________ and therefore totally _______________.
X-‐components
There is no ________________ working on the projectile in the X and the acceleration is always _____________. Therefore the only equation we can ever use is:
The only value that can ever be used on both sides is ____________ because it is a ______________ .
Y-‐components
In this case there is always a constant acceleration of _______________________. Because of this we need to use the _______________________.
Horizontal Projectile Problem: A student sits on the roof of their house, which is 12 m high. She can launch water-‐balloons from a slingshot at 14.0 m/s. If she fires a water-‐balloon directly horizontally:
a. How long will it be airborne? This depends on:
b. How far forward will it travel? This depends on:
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Horizontal Projectile Problems
1. A rock is thrown horizontally from the top of a cliff 98 m high, with a horizontal speed of 27 m/s.
(a) For what interval of time is the rock in the air? (b) How far from the base of the cliff does the rock land? (c) With what velocity does the rock hit?
2. A rescue pilot wishes to drop a package of emergency supplies so that it lands as close as possible to a target. If the
plane travels with a velocity of 81 m/s and is flying 125 m above the target, how far away (horizontally) from the target must the rescue pilot drop the package?
3. A bullet is fired with a horizontal velocity of 330 m/s from a height of 1.6 m above ground. Assuming the ground is level how far from the gun will the bullet hit the ground?
4. A firefighter is standing on top of a building 20.0 m high. She finds that if she holds the hose so that water issues from it horizontally at 12 m/s, the water will hit a burning wall of an adjacent building at a height of 15.0 m above the ground. What is the horizontal distance from the firefighter to the building?
5. An arrow is fired horizontally with a speed of 25.0 m/s from the top of a 150.0-‐m-‐tall cliff. Assuming no air
resistance, determine the distance the arrow will drop in 2.50 s. 6. A skier leaves the horizontal end of a ramp with a velocity of 25.0 m/s [E] and lands 70.0 m from the base of the
ramp. How high is the end of the ramp from the ground?
Example: A Cutlass Supreme drives straight out of a parking garage at 8.0 m/s and hits the water 3.4 s later.
a. How far did the car fall?
b. What was his total impact velocity? (magnitude and direction)
1) a. 4.5 s b. 120 m c. 51 m/s 58o BTH 2) 410 m 3)190 m 4) 12 m 5) 30.7 m 6) 38.5 m