You travel 800 km in 20 hours. What is your average speed
The odometer of a car reads 20.km at the beginning of a trip and 180km at the end of the trip. It took 2.0 hours and 30. minutes to make the entire trip. What was the average speed
Would it be possible to keep this average speed and not exceed 64km/h
Velocity - speed in a given direction
Must have two components
Speed or Velocity
4.5 miles per hour west
7.3 m/s northeast
A car travels east at 55mi/h. Another car travels north at 55mi/h.
Do the cars have the same speed
Do the cars have the same velocity
Constant Velocity 2 requirements
Constant Speed (no faster no slower)
Constant Direction (straight line path)
Either speed or direction or both are changing
Constant speed along a curved path is changing velocity because the direction is changing at every instant
In a car there are three controls that change the velocity
10 Graphs of MotionUniform Velocity
Describing motion using a position (distance) vs time graph
Consider a car moving east with a velocity of 10m/s
The graph is linear because the velocity is constant
The slope of a position vs time graph is the velocity.
11 Graphs of MotionUniform Velocity
Describing motion with velocity vs time graphs
Consider a car moving east with a positive constant velocity of 10m/s.
The velocity is constanttherefore the graph is a horizontal line.
The slope of a velocity vs time graph is acceleration. Velocity is constanttherefore the slope is 0 (there is no acceleration)
12 Graphs of Motion
Velocity vs time graphs How can you tell if it is moving in a positive direction
The velocity is positive whenever the graph is in the positive region.
The velocity is negative whenever the graph is in the negative region.
13 Distance or Displacement
Distancehow far an object has traveled
Indianapolis is about 45 miles away
The distance to Indianapolis is 45 miles the distance back to Bloomington is 45 milesthe total distance traveled round trip is 90 miles
Displacementhow far an object is from its original position (direction matters)
The displacement to Indianapolis is 45 miles north the displacement back to Bloomington is 45 miles souththe total displacement is 0 miles
You can find displacement by
Finding the area under a velocity time graph
Using the equation d vavg t
14 Graphs of MotionSlope
Looking at the slope of a position (distance) vs time graph...
As slope goes so does velocity.
If the velocity is constant then the slope is constant (straight line).
If the velocity is changing then the slope is changing (curve).
If the velocity is positive then the slope is positive (moving upward towards the right).
If the velocity is negative then the slope is negative (moving downward towards the right).
The steeper the line/curve the faster the velocity.
Looking at the slope of a velocity vs time graph
If the graph is a horizontal line there is no change in velocity therefore there is no acceleration (the slope is 0).
If the acceleration is positive then the slope is positive (the line moves upward to the right).
If the acceleration is negative then the slope is negative (the line moves downward to the right).).
15 Graphs of MotionUniform Velocity
The area under a velocity vs time graph is the displacement of the object.
Find the distance traveled by each object.
Acceleration the rate at which velocity is changing
Acceleration v/ t
Can increase or decrease (sometimes called deceleration)
Think of traveling in a car you can feel the acceleration
3 ways to accelerate in a car
Brake pedalslowing down coming to a stop (changing speed)
Steering wheelgoing around a corner or curve (changing direction)
Gas pedalleaving from a stopped position (changing speed)
Suppose you are traveling in a car and your speed goes from 10.km/h to 60.km/h in 2.0s. What is your acceleration
Suppose a car goes from 80.km/h to 15km/h in 5.0 seconds. What is the acceleration
A car is coasting backwards down a hill at a speed of 3.0m/s when the driver gets the engine started. After 2.5s the car is moving uphill at 4.5m/s. Assuming that uphill is in the positive direction what is the cars average acceleration
18 Graphs of MotionUniform Acceleration
Consider a car moving east with a changing velocitythe car is accelerating (speeding up).
The velocity is changingtherefore the line has a slope (acceleration)
19 Graphs of MotionUniform Acceleration
Now consider a car moving east that is accelerating. Notice the different graph.
The car is acceleratingtherefore the velocity (slope) is not constant and the graph is a curve not a line
20 Graphs of Motion
Velocity vs time graphs How can you tell if the object is accelerating or decelerating
Accelerating (speeding up) when the magnitude of the velocity is increasing
Decelerating (slowing down) when the magnitude of the velocity is decreasing
21 Free FallA Case of Uniform Acceleration
What makes an object fall
Gravitythe mass of the Earth is so great is has a strong gravitational pull that pulls objects to it
Gravity also allows you to stand on the Earth without floating off into free space
Gravity is the cause for satellite moon and planet orbits
Do heavier objects fall faster than lighter ones
Galileo found that neglecting the effects of air all freely falling objects had the same acceleration
Masses do not matter
Drop height does not matter
The acceleration of a falling object is gravity (g) 9.80m/s2 (on Earth). We will use g 10 m/s2 in most of our calculations (except for in labs or any other time when accuracy matters)
Free Fall objects affected only by gravity
22 Free Fall
An object in free fall accelerates at 10 m/s2
The objects velocity increases by 10 m/s each second.
Because the object is accelerating the distance it falls each second increases
23 Free Fall How far How fast 24 Free Fall
A rock is dropped off a bridge and hits the water 2.3 seconds later. The rock accelerates due to gravity at a rate of 10 m/s2.
Using the water as the zero position and calling the upward direction positive draw position-time velocity-time and acceleration-time graphs for the rock.
What is the rocks speed just before hitting the water
Determine the height of the bridge.
King Kong carries Fay Wray up the 321 meter tall Empire State Building. At the top of the skyscraper Fay Wrays shoe falls from her foot. How fast will the shoe be moving when it hits the ground
Kinematics is the science of describing the motion of objects using words diagrams numbers graphs and equations.
vf vo at vf2 vo2 2ad
d vot ½ at2 d (vo vf)t/2
Displacement how a far an object has moved from its original position (d)
Velocity the speed of an object in a given position (vf final velocity vo initial velocity)
Acceleration the rate at which an object changes velocity (a)
Solving Kinematics Problems
Write down all the variables that are given to you what you need to solve for
Compare these to the four kinematics equations to determine which equation should be used
Be sure to use significant figures
When computing (more than one operation) always round to one more sig fig than necessary until you achieve your final answer.
26 Linear Kinematics Problems
Vivian is walking to the hairdressers at 1.3m/s when she glances at her watch and realizes that she is going to be late for her appointment. Vivian gradually quickens her pace at a rate of 0.090m/s2. What is Vivians speed after 10.s
A race car traveling at 44m/s slows at a constant rate to a velocity of 22m/s over 11s. How far does it travel over this time
27 Linear Kinematics Problems
If a car accelerates from rest at a constant 5.5m/s2 how long will it need to reach a velocity of 28m/s
A car accelerates at a constant rate from 15m/s to 25m/s while it travels 125m. How long does it take to achieve this speed
28 Linear Kinematics Problems
A driver of a car traveling at 15.0 m/s applied the brakes causing a uniform acceleration of -2.0 m/s2.
How long does it take the car to accelerate to a final speed of 10.0 m/s
How far has the car moved during the braking period
A boat accelerates uniformly from a velocity of 6.5 m/s to the west to a velocity of 1.5 m/s to the west. If its acceleration was 2.7 m/s2 to the east how far did it travel during the acceleration
29 Kinematics Problems (Free Fall)
The steamboat geyser at Yellowstone National Park Wyoming is capable of shooting hot water up from the ground with a speed for 48.0m/s. How high can the geyser shoot
2. A giraffe which stands 6.00m tall bites a branch off a tree to chew on the leaves and he lets the branch fall to the ground. How long does it take the branch to hit the ground
30 Kinematics ProblemsFree Fall
3. An object is thrown straight up with a velocity of 30.0m/s.
As the object moves up its acceleration is -10m/s2. For the velocity to be at zero how long must the object be in the air
Is the acceleration 0 when the instantaneous velocity is 0
What is the acceleration of the object when it is on its way down
When are the instantaneous speeds the same
Are the velocities the same at this time
4. A person throws a rock with an initial velocity of 14 m/s straight down off of a cliff. It takes 10.0 s for the rock to hit the ground.
What is the rocks velocity as it hits the ground
How far does the rock travel
31 Air Resistance and Falling Objects
Feather vs Book
Suppose you drop a feather and book from the top of the school at the same time
Which will land first
Without air resistance they would both land at the same time.
The effect of air resistance on the feather is so great the book will land well before the feather.
Which has the greatest air resistance
The book has a greater area and mass therefore it displaces more air than the featherexperience greater air resistance.
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