Motion. Two parts of describing motion ◦ 1. Speed ◦ 2. Direction.
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Transcript of Motion. Two parts of describing motion ◦ 1. Speed ◦ 2. Direction.
Definition - A system of objects that are not moving with respect to one another
Frame of Reference
Relative Motion• Definition – Movement in relation to a
frame of reference– For example, does a person sitting on a
moving train have motion? It all depends on the frame of reference
The length of a path between two points
In other words, distance is the length of a path connecting an objects starting point and its ending point
SI unit for distance is the meter
Distance
Definition – The direction from the starting point and the length of a straight line from the starting point to the ending point
Example – What would your displacement be if you rode a rollercoaster?
Displacement
If you hit a home run in baseball, you would run from home plate, to each of the bases (1 through 3) and then back to home plate. If there is a distance of 30 meters between each of the bases, what is the total distance you run? What is your displacement?
Baseball Example
Definition – A quantity that has both magnitude (size, length or amount) and direction
Represented using arrows
Displacement is an example of a vector
Vector
When two displacements have the same direction, you can add their magnitudes
4 km E + 2 km E = 6 km E
Displacement along a straight line
0 1 2 3 4 5 6
4 km2 km
When two displacements have opposite directions, you can subtract their magnitudes
4 km E + 2 km W = 2 km E
Displacement along a straight line
0 1 2 3 4 5 6
4 km
2 km
When two or more vectors have different directions, they may be combined using graphing.
Displacement that is not along a straight line
The vector sum of two or more vectors
Can be used to show total displacement
Points directly from starting point to ending point
Resultant Vector
The ratio of the distance an object moves to the amount of time the object moves.
SI UNIT◦ Meters per second, or m/s
Speed
Two types of speed
Average Speed Instantaneous Speed
Computed for the entire duration of the trip
Speed may change from moment to moment, but this tells you the average speed over an entire trip
Measured at a particular moment in time
Example: The speedometer in a car provides instantaneous speed
Average speed =
Or
◦ v = average speed◦ d = total distance traveled ◦ t = total time
v=
Average SpeedTotal Distance
Total Time
dt
While traveling on vacation, you measure the times and distances you travel. You travel 35 kilometers in 0.4 hours, followed by 53 kilometers in 0.6 hours. What is your average speed?
d = 35 km + 53 km = 88 kmt = 0.4 h + 0.6 h = 1.0 h
Average Speed Example 1
A person jogs 4.0 km in 32 minutes, then 2.0 km in 22 minutes, and finally, 1.0 km in 16 minutes. What is the jogger’s average speed in kilometers per minute? In km/ hour?
Average Speed Example 2
Use can use a distance-time graph to describe motion
Reminder – SLOPE◦ the change in the vertical axis value divided by
the change in the horizontal axis value
On a distance-time graph, slope is the change in the distance divided by the change in time (or speed)
Graphing Motion
A description of both speed and direction of motion
Velocity, like displacement, is a vector because it has both magnitude and direction
Velocity
Two or more velocities add by vector addition
When two velocities have the same direction, you can add their magnitudes
Combining Velocities
A man on the ground observes a train passing by. Through the train windows he sees a man running in the same direction as the train is moving. What is the apparent velocity of the man running on the train if the train is moving at 30 km/h and the man is running at 5 km/h?
Train Example
A plane is moving south at 100 km/hour. Wind is blowing from the east at 25 km/ hour. What is the resultant velocity of the plane? (HINT – draw a picture to help visualize the problem)
Plane Example
The rate at which velocity changes
Changes in:◦ Speed◦ Direction◦ Or both speed & direction
Acceleration is a vector (it has both magnitude and direction)\
SI Unit – meters per second per second (m/s2)
What is acceleration?
An acceleration that slows an objects speed
Negative acceleration
Example◦ As your car approaches a red light you step on
the break pedal to slow the car down. This causes the velocity of the car to change (it decreases) and thus the car decelerates.
Deceleration
The movement of an object toward Earth solely because of gravity
Objects falling near Earth’s surface accelerate downward at a rate of 9.8 m/s2
Free Fall
Each second an object is in free fall, its velocity increases downward by 9.8 m/s
Free Fall (Continued)t = 0sv = 0 m/s
t = 1sv = 9.8 m/s
t = 2sv = 19.6 m/s
t = 3sv = 29.4 m/s
You can accelerate even if your speed is constant because acceleration also includes changes in direction
Example◦ If you ride a bike around a curve and maintain the
same speed, acceleration changes because your direction changes
Changes in Direction
Green Lantern Front Seat (Six Flags)
Describe the acceleration of the roller coaster as it reaches and just overcomes the first hill.
Roller Coasters…
A steady change in velocity
The velocity of an object moving in a straight line changes at a constant rate
Constant Acceleration
For straight-line motion:
Calculating Acceleration
Acceleration = Change in Velocity
Total Time
A = tvf - vi
vf = Final Velocityvi = Initial Velocity
What is the magnitude of the skydiver’s acceleration after 1 second? Between 2 and 3 seconds?
Acceleration Example #1t = 0sv = 0 m/s
t = 1sv = 9.8 m/s
t = 2sv = 19.6 m/s
t = 3sv = 29.4 m/s
A ball rolls down a ramp, starting from rest. After two seconds, its velocity is 6 m/s. What is the acceleration of the ball?
Acceleration Example #2
A = tvf - vi
Group Practice Activity
Complete the problem assigned to your group. You will be presenting your answer to the class.
A car traveling at 10 m/s starts to decelerate steadily. It comes to a complete stop in 20 seconds. What is its acceleration?
An airplane travels down a runway for 4.0 seconds with an acceleration of 9.0 m/s2. What is its change in velocity during this time.
A child drops a ball from a bridge. The ball strikes the water under the bridge 2.0 seconds later. What is the velocity of the ball when it strikes the water? (Hint: Think “FREE FALL”)
A boy throws a rock straight up into the air. It reaches the highest point of its flight after 2.5 seconds. How fast was the rock going when it left the boy’s hand? (Hint: Think “FREE FALL”)
The slope of a speed-time graph is acceleration
What is the formula for slope of a line?
Speed-Time Graphs
Time TimeTime
Sp
eed
Sp
eed
Sp
eed
Increasing Acceleration
Constant Acceleration
Decreasing Acceleration