Motion. Some Motion Terms Distance & Displacement Velocity & Speed Acceleration Uniform motion...
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Transcript of Motion. Some Motion Terms Distance & Displacement Velocity & Speed Acceleration Uniform motion...
Motion
Some Motion Terms
Distance & DisplacementVelocity & SpeedAccelerationUniform motionScalar .vs. vector
Scalar versus Vector
Scalar - magnitude only (e.g. volume, mass, time)
Vector - magnitude & direction (e.g. weight, velocity, acceleration)
Pictorial Representation
An arrow represents a vector – Length = magnitude of vector– Direction = direction of vector
Pictorial Representation
This arrow could represent a vector of magnitude 10 point to the “right”
This arrow could represent a vector of magnitude 5 point to the “left”
Distance & Displacement
Distance is the actual distance traveled.
Displacement depends only on Start & Finish line
Displacement is the distance traveled , in a certain direction.
Displacement Isn’t Distance
The displacement of an object is not the same as the distance it travels– Example: Throw a ball straight up and then
catch it at the same point you released it The distance is twice the height The displacement is zero
Distance & Displacement
Distance & Displacement
B
A
C
5 m
4 m
3 m
You walk from A to B to C.Your distance traveled is 7mYour displacement form A is 5 m
Velocity & Speed
Velocity is the displacement traveled in a certain time.
Speed is the distance traveled in a certain time.
Velocity is speed in a given direction.
Instantaneous Speed is the speed at any specific instance
Average Speed is the total distance covered divided by total time
Types of Speed
Speed
The average speed of an object is defined as the total distance traveled divided by the total time elapsed
– Speed is a scalar quantity
Average speed total distance
total time
Speed d
t
Velocity
The average velocity of an object is defined as the total displacement traveled divided by the total time elapsed
– Velocity is a vector quantity
Average velocity total displacement
total timeV
x
t
Speed, cont
Average speed totally ignores any variations in the object’s actual motion during the trip
The total distance and the total time are all that is important
SI units are m/s
Velocity
It takes time for an object to undergo a displacement
The average velocity is rate at which the displacement occurs
generally use a time interval, so let ti = 0
Vaverage xt
x f x it f ti
x f x it
Velocity continued
Direction will be the same as the direction of the displacement (time interval is always positive)– + or - is sufficient
Units of velocity are m/s (SI), cm/s (cgs) or ft/s (US Cust.)– Other units may be given in a problem, but
generally will need to be converted to these
Speed vs. Velocity
Cars on both paths have the same average velocity since they had the same displacement in the same time interval
The car on the blue path will have a greater average speed since the distance it traveled is larger
Speed vs. Velocity
You drive from Yakima to Seattle (140 miles away) You stop in Ellensburg for a 2 hr lunch with a
friend. Your total driving time is 2 hours
Average speed 140 miles
2 hour 2 hour
Average speed 140 miles
4 hours35 mph
Uniform Velocity
Uniform velocity is constant velocity The instantaneous velocities are always
the same – All the instantaneous velocities will also
equal the average velocity
Velocity Example
150 Km/hr
100 Km/hr
50 Km/hr
How fast is the plane moving in respect to the ground? 100 Km/hr
Wind35 Km/hr
Velocity again
How fast is the plane moving in respect to the ground? 100 Km/hr
Wind35 Km/hr
Velocity, yet again
How fast is the plane moving in respect to the ground?
100 Km/hr
Wind35 Km/hr
Result
65 Km/hr
Velocity (finally)
How fast is the plane moving in respect to the ground?
100 Km/hr
50 Km/hrWind
Velocity again (??)
How fast is the plane moving in respect to the ground?
100 Km/hr
50 Km/hrWind
Resultant
a2
b2c2
a2 b2 c2+ =
Velocity - the last time
How fast is the plane moving in respect to the ground?
100 Km/hr
50 Km/hrWind
Resultant
a2
b2c2
a2 b2 c2+ =
R2 = (100)2 + (50)2 R2 = 10,000 + 2500 R2 = 12,500R = 111.8 Km/hr
(Last) Velocity…
Acceleration
Change in velocity divided by the change in time
a Vt
Acceleration
Changing velocity (non-uniform) means an acceleration is present
Acceleration is the rate of change of the velocity
Units are m/s2 (SI), cm/s2 (cgs), and ft/s2 (US Cust)
Average Acceleration
Vector quantity When the sign of the velocity and the
acceleration are the same (either positive or negative), then the speed is increasing
When the sign of the velocity and the acceleration are in the opposite directions, the speed is decreasing
Instantaneous & Uniform Acceleration
The limit of the average acceleration as the time interval goes to zero
When the instantaneous accelerations are always the same, the acceleration will be uniform– The instantaneous accelerations will all be
equal to the average acceleration
Relationship Between Acceleration & Velocity
Uniform velocity (shown by red arrows maintaining the same size)
Acceleration equals zero
Relationship Between Velocity & Acceleration
Velocity and acceleration are in the same direction
Acceleration is uniform (blue arrows maintain the same length)
Velocity is increasing (red arrows are getting longer)
Positive velocity and positive acceleration
Relationship Between Velocity & Acceleration
Acceleration and velocity are in opposite directions
Acceleration is uniform (blue arrows maintain the same length)
Velocity is decreasing (red arrows are getting shorter)
Velocity is positive and acceleration is negative
Kinematic Equations
Used in situations with uniform acceleration
V f V0 at
V f2 V0
2 2ax
x x0 V0t 12 at
2
Kinematic Equations - Ex #1
A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s2, for 6 seconds. What is the car’s final velocity?
Kinematic Equations - Ex #1 - Ans
A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s2, for 6 seconds. What is the car’s final velocity?
V f V0 at
V f 6m
s 2m
s2 6s18m
s
Kinematic Equations - Ex #2
A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s2, for 6 meters. What is the car’s final velocity?
Kinematic Equations - Ex #2 - Ans
A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s2, for 6 meters. What is the car’s final velocity?
V f2 V0
2 2ax
V f2 6
m
s
2
2 2m
s26m
V f2 36
m2
s2 24
m2
s260
m2
s2
V f 60m2
s27.746
m
s
Kinematic Equations - Ex #3
A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s2, for 6 sec. How far does the car travel?
Kinematic Equations - Ex #3 - Ans
A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s2, for 6 sec. How far does the car travel?
x xo V0t 1
2at 2
x 0 6m
s6s
1
22m
s2 6s 2
x 0 36m 36m72m
Galileo Galilei
1564 - 1642 Galileo formulated
the laws that govern the motion of objects in free fall
Also looked at:– Inclined planes– Relative motion– Thermometers– Pendulum
Free Fall
All objects moving under the influence of gravity only are said to be in free fall– Free fall does not depend on the object’s
original motion All objects falling near the earth’s
surface fall with a constant acceleration The acceleration is called the
acceleration due to gravity, and indicated by g
Acceleration due to Gravity
Symbolized by g g = 9.81 m/s2
g is always directed downward– toward the center of the earth
Ignoring air resistance and assuming g doesn’t vary with altitude over short vertical distances, free fall is constantly accelerated motion
Free Fall – an object dropped
Initial velocity is zero Let up be positive Use the kinematic
equations– Generally use y instead of x
since vertical Acceleration is g = -9.81
m/s2
vo= 0
a = g
Free Fall – an object thrown downward
a = g = -9.81 m/s2
Initial velocity ≠ 0– With upward
being positive, initial velocity will be negative
vo 0
a = g
Free Fall - example
If a rock is dropped from a
building, and it takes 18 seconds to reach the ground, how tall is the building?
Free Fall - answer
V0 0m
sV f ??
x ??
a 9.81m
s2
t 18sec
•What do we know?
Free Fall - answer
x(t) x0 V
0t
1
2at2
x(t) 0 0 1
2(-9.81
m
s2)(18 sec)
2
x(t) 1587.6 meters 0.986 miles
Motion
The End