Kinematics 1D -

taupeselectionMechanics

Nov 14, 2013 (3 years and 11 months ago)

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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: