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Kinematics

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Mr. Emhardt

on 8 September 2016

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Transcript of Kinematics

Kinematics
Mr. Emhardt
Regents Physics

Terminology
Mechanics - Study of the relationship between force and motion

I. Kinematics - Mathematical methods of describing and predicting motion




Average Speed
how much distance an object covers per unit time
Average Speed of 120 miles per hour can also be written 120 miles/hr
per = divided by
Could mean traveled
120 miles in one hour
OR ....
60 miles in 1/2 hour (30 minutes)


Calgary, Canada has a speed limit of 100
Importance of units km/hr

100km/hr ~ 60 mph

(about 28 m/s)
Average Speed
Speed Units: Meters per second (m/s)
or
kilometers per hour (km/h)
FORMULA

Variable
Units
d
t
An object travels 5 meters in 2 seconds.

Find its speed.
Example
Example
An object moves at a rate of 3 m/s for 1.5 seconds.

How far did the object move?
Example
An object moves at rate of 4 m/s over a distance of 10 meters.

How long did it take to travel that distance? t = ?
A
B
C
t=0s
d=0m
t=23s
d=89m
t=100s
d=321
Find the average velocity from A to B
Warm-Up

A car travels at a constant speed from 39 meters to 192 meters in 34 seconds. Calculate the car's average speed.
Warm-Up
Find the average speed of the object from 0-5 sec and from 5 secs to 10 sec
Displacement
Scalar - Distance
Vector - Displacement
Displacement- distance and direction from start to finish

Scalar and Vector Quantities
Scalar- a quantity that includes MAGNITUDE only

Vector- a quantity that includes MAGNITUDE and DIRECTION

Magnitude - a number
Direction - north, east, south, west, up, down, left, right, +, -
Distance =
Displacement =
Velocity
Speed in a particular direction
Speed (scalar)
Velocity (vector)
Warm-up
Describe the motion
a
b
c
d
1
2
time rate of change in velocity (how quickly velocity is changing)
Acceleration
Acceleration = 2 m/s/s
Acceleration = 3 m/s/s
Acceleration = 0 m/s/s
Acceleration = -1 m/s/s
2 ways to have zero acceleration
Remain at rest
or
travel at a constant velocity
Acceleration EQUATION


Starting Velocity: 5m/s West
Final Velocity: 25 m/s West
Time during speed change: 5 secs
Starting Velocity: 20m/s West
Final Velocity:5 m/s West
Time: 5 seconds
3 ways to have non-zero acceleration
Speed Up
Slow Down
Change Direction
Motion Plots
slope = speed
Distance vs. time
Motion Plots
Velocity vs. Time
Displacement on a V vs. T graph
Find area under the curve
Describe motion using
y axis and slope
Step 1: y axis =
Step 2: slope =
Calculate
distance traveled after 2s, 4s, 6s
the velocity
the acceleration
Calculate
Velocity at 2s, 4s, 6s, 8s,
Acceleration
Motion Equations for Problem Solving
Free Fall
Questions to ponder

1. Describe the motion of a falling body.

2. What are the forces affecting the motion of a falling body?

3. In the absence of air friction, how would the acceleration of a large mass compare with the acceleration of a small mass?
Freefall - falling where the only force is gravity
How long will it take for the ball to reach the peak and fall back to it's original position?
An object is thrown up at a velocity of 30 m/s

About how long will it take to hit the ground?
…an object is dropped
Vi = 0
a = g = +9.8m/s
(make down +)

… an object is ascending:
a = g = -9.8 m/s
(make down -)
2
2
A coin is dropped in a vacuum tube, find its displacement after .30 seconds.
A coin is dropped in a vacuum tube, find the coin's velocity after .30 seconds
A rocket is fired vertically upward with an initial velocity of 29 m/s.
Find the rocket's maximum altitude.
Free Fall Motion
Using complete sentences and proper physics vocabulary write a paragraph that describes an object's motion that is in free fall.

This will be turned in.
Free Fall Graphs
An object in free fall is undergoing a constant acceleration.
If we start from the top...
d
t
v
t
Free Fall Graphs
An object thrown upwards is undergoing a constant negative acceleration
d
t
v
t
0

- have 2 velocities Vx, Vy
- Vx is determined by thrower
- Vx constant (neglect fricition)
- Viy = 0 (initial vert. vel.)
- Vy changed by gravity
Objects Propelled Horizontally
Vocabulary
Displacement
- Distance traveled from start to finish, always a straight line shortest length. (VECTOR)
Distance
- Measure of how far something moves (SCALAR)
Scalar
-
Speed
- Measure of how far something moves over a given period of time (SCALAR)
Vector
-
Velocity
- Speed with a direction associated with it (VECTOR)

Distance ?
A student travels 120 m north in 37 seconds. They then turn around and travel 100 m south in 20 s.
a) Calculate the average speed for the entire journey
b) Calculate the average velocity for the entire journey
A student travels 120 m north in 37 seconds. They then turn around and travel 100 m south in 20 s.
a) Calculate the distance of the journey
b) Calculate the displacement of the journey
Starting Velocity: 10m/s West
Final Velocity:42 m/s West
Acceleration: 3.2 m/s/s West
Starting Velocity: 8m/s West
Acceleration: 2.6 m/s/s West
Time: 5 seconds
Motion Plots
Graphs that describe the motion of an object
must read y and x axis
determine slope of the line
Straight line show constant slope
Curved line shows a changing slope
Motion Plots
Five Slopes to Remember
Constant slope Positive direction
Constant slope
Negative direction
Constant Zero
Increasing
(positive change)
Decreasing
(negative change)
Slope Formula m =
y - y
x - x
f
f
i
i
a
b
c
d
a to b
b to c
c to d
Slope = acceleration

B to C ?
A to C ?
An object that is originally moving at a speed of 20. meters per second accelerates uniformily for 5.0 seconds to a final speed of 50. meters per second. What is the acceleration of the object?
Warm-up Quiz (turn in)
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