Kinematics 1D

Motion

Types of Motion
Ticker Tape Diagram
Motion Graphs
d
t
v
t
d
t
v
t
d
t
v
t
d
t
v
t
Slope =
Slope =
Defining Position

Scalar

Vector

Distance

Displacement
:
Δ
d =
d
f
–
d
i
Speed

Velocity

A baseball player hits a homerun. It is 90ft to each base and
the batter rounds the bases ending back at home plate…
Q: What was the batters distance traveled and total displacement?
Examples
Examples
Vector Diagrams 1D
Ex 1)
Distance =
Displacement =
Speed =
Velocity =
Ex 2)
Distance =
Displacement =
Speed =
Velocity =
Ex 3)
Distance =
Displacement =
Speed =
Velocity =
Ex 4)
Distance =
Displacement =
Speed =
Velocity =
Can distance and displacement be the same thing? If so, then when and what does that mean for
speed and velocity under the same conditions?
Time = 10s for all
Vector Diagrams 2D
Distance
vs
Displacement
Greater Distance: A
B
Greater Displacement: A B
Q:
If
d
A
= 1500m and d
B
= 500m, how
fast would A have to travel to reach
peak at the same time as B?
Ex 1)
Pythagorean Theorem

Trigonometry

For each scenario, determine the resultants magnitude and direction…
Ex 2)
Dist =
Disp
=
V =
Vector Components & Resultants…
Displacement Vectors
Velocity Vectors
A dog runs 50m @ 40⁰ North of East..
A plane flies East at 100m/s while a wind blows
North at 50m/s..
What are the x and y components?
What is the resultant velocity of the plane?
Graphically
: Using a scale of 1cm = 10m
Graphically
: Using a scale of 1cm = 25m/s
Analytically:
Analytically:
E
N
Motion Graphs
Displacement
vs
Time (d vs. t)
Velocity vs. Time (v vs. t)
Slope =
Slope =
Area =
d
v
t
t
A

At rest
B
–
Slow const velocity
C
–
Fast const velocity
D
–
Speeding Up
E
–
Slowing down
Acceleration
vs
Time (a vs. t)
a
t
a
t
d
t
v
t
Kinematics Equations:
Average Velocity:
Q1
: What is the average velocity of the marble?
Q2:
Was the marble moving at constant velocity?
Q3:
What was the final velocity of the marble?
A marble starts from rest and rolls down a 1.5m incline in ______s …
Acceleration:
Q4
: What was the acceleration of the marble?
Distance Formula:
Q5:
Confirm that the marble rolled 1.5m.
Final Velocity Formula:
Q6:
Confirm the final velocity.
Problem Solving Using Kinematics Equations
Analyze
–
underline important and relevant
information. (quantities, direction etc)
Given/Find
–
list the given and find information
to help determine which equation to use
Equation
–
write down the equation necessary to
solve the problem
Algebra
–
use algebra (if necessary) to isolate the
variable you are solving for
Substitution
–
fill the given quantities into the
equation WITH UNITS!!!!!!
Answer
–
label your answer WITH UNITS and box in
A marble is given a push so that it rolls up an incline. The marble was given an initial velocity of 4m/s
and rolls 2m in 1.2s. Assuming that ‘up the incline’ is considered the (+) direction. Determine the
acceleration of the marble.
Uniform Accelerated Motion
A rocket ship in outer space sits motionless at rest. Then suddenly the engines ignite and the space ship begins to
accelerate uniformly (at constant rate). After accelerating for 5s, the spaceship is traveling at 100m/s…
Time (s) Velocity(m/s)
Displacement (m)
Equation used
Equation used
0
1
2
3
4
5
6
7
8
Q1) At what rate does the space
ship gain velocity?
Q2) Draw a ticker tape diagram of
the space ships motion.
Q3) Complete the data chart..
Q4) Does the spaceship move the
Same distance for each given
second? Explain..
∆d
∆d
∆d
∆d
∆d
∆d
∆d
∆d
Directions:
Fill
in the values for the velocity for each second..
0m
100m
200m
300m
400m
500m
600m
700m
800m
t
0
t
1
t
2
t
3
t
4
t
5
t
6
t
7
t
8
Sketch the d

t and v

t graphs for the motion of the space ship
d
v
t
t
Q) How far did the space ship go between the time interval 4 and 8 seconds?
Horizontal Kinematics

A car ride
Q1) What is the final velocity after 10s?
Q2) How far did the car go during this time?
Q3) How long did it take to travel this distance?
A car accelerates from rest at a constant rate of
2m/s
2
for 10s in the positive direction…
d
t
v
t
The car then cruises at a constant velocity for 1000m…
The car then slams on the breaks coming to a skidding
stop in 10m…
Q4) What was the deceleration of the car?
Q5) How long did it take to come to a stop?
Q6) What was the average velocity of the car during breaking?
Vertical Kinematics

Free Fall Motion
Neglecting air friction…
a
Dropped from rest, what velocity does an
object have after falling…
1s…
2s…
3s…
4s…
A rock is dropped off of a cliff 100m tall.
.
Q1) How long until the rock hits the ground?
Q2) How fast does it hit the ground?
Q3) How fast would rock hit ground if it was thrown
downward at 5m/s?
What would the motions graphs look like for a rock thrown
upwards and landing back where it started?
d
t
v
t
Note:
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