Its all about Kinematics Equations Kinematic Equations the branch of mechanics concerned with the motion of objects without reference to the forces that cause the motion Two types of Equations Constant Velocity Equations acceleration 0 ID: 621256
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Kinematics EquationsSlide2
Its all about Kinematics Equations
Kinematic Equations
the branch of mechanics concerned with the motion of objects without reference to the forces that cause the motion.
Two types of Equations
Constant Velocity Equations (acceleration = 0)
Constant Acceleration questions (velocity is constantly changing) (a≠0 but is a constant…the same) Slide3
Uniform Motion Equations (
=0)
Δv=
Δ
x/Δt (y instead of x for vertical)
Δvavg=xtotal/Δt total (book uses for avg velocity)Note: constant velocity means vinst =vavgxf=xi+vavgΔt (y for vertical)
Slide4
Displacement with Constant Acceleration
Recall that for an object moving at a constant velocity, displacement is equal to average velocity times the time interval.
x=
vt
For an object that is changing velocity and uniformly accelerating, the average velocity can be written.
Therefore:
x
t
Slide5
Velocity with Average Acceleration
If an object’s
average acceleration
during a time interval is known, the
change in velocity
during that time can be found. The definition of average acceleration
Solving for final velocity:
t
Slide6
Displacement with Constant Acceleration
In cases in which the
acceleration
is constant, the
average acceleration,
, is the same as the instantaneous acceleration, a. The equation for final velocity can be rearranged to find the time at which an object with constant acceleration has a given velocity.
Δt Slide7
Displacement with Constant Acceleration
If the
v
i
, a and Δt are known, the displacement can be found by combining….V
f=vi+aΔt
Δ
tSubstituting the equation for vf into the 2nd equation results in:(I did not use the Δ for t but its there!!! Book does this all the time)x
or xf = x
0 +
Slide8
Displacement with Constant Acceleration
Solve this equation
v
f
= vi+ at
for time….∆t
Substituting the equation for “
t”
intox
∆t RESULTS IN:
∆x
(this is known as the “timeless equation”)
Slide9
The Fab Four of Kinematics
∆t
∆t
x
f
I use x and y depending on horizontal or vertical. Many times the ∆ is missing but its there!!!
Slide10
Oh so important little table!!!!
© 2014 Pearson Education, Inc.Slide11
Question 1: Coming to a stop
As you drive in your car at 15 m/s (just a bit under 35 mph), you see a child’s ball roll into the street ahead of you. You hit the brakes and stop as quickly as you can. In this case, you come to rest in 1.5 s. How far does your car travel as you brake to a stop?Slide12
Question 1: Coming to a stop
Draw the pictures (particle motion and V-T)
Do not forget the v and a vectors Slide13
Question 1 Answer
Acceleration:
Distance Traveled
:
© 2015 Pearson Education, Inc.Slide14
Question 2: Kinematics of a rocket launch
A Saturn V rocket is launched straight up with a constant acceleration of 18 m/s
2
. After 150 s, how fast is the rocket moving and how far has it traveled?
© 2015 Pearson Education, Inc.Slide15
Question 2: Kinematics of a rocket launch (cont.)
© 2015 Pearson Education, Inc.
Speed:
Distance Traveled:Slide16
Question 3: Calculating the minimum length of a runway
A fully loaded Boeing 747 with all engines at full thrust accelerates at 2.6 m/s
2
. Its minimum takeoff speed is 70 m/s. How much time will the plane take to reach its takeoff speed? What minimum length of runway does the plane require for takeoff? USE YOUR WORKSHEET
DRAW THE PICTURE!!!!!Slide17
Question 3: Calculating the minimum length of a runway (cont.)
Time:
© 2015 Pearson Education, Inc.Slide18
Question 3: Calculating the minimum length of a runway (cont.)
Runway Length:
© 2015 Pearson Education, Inc.Slide19
QUESTION 4
A position-time graph of a bike moving with constant acceleration is shown on the right. Which statement is correct regarding the displacement of the bike?
A. The displacement in equal time interval is constant.
B. The displacement in equal time interval progressively increases.
C. The displacement in equal time interval progressively decreases.
D. The displacement in equal time interval first increases, then after reaching a particular point it decreases.Slide20
Example Problem (if We have time): Champion Jumper
The African antelope known as a
springbok will occasionally jump straight
up into the air, a movement known as a
pronk
. The speed when leaving the ground can be as high as 7.0 m/s.If a springbok leaves the ground at 7.0 m/s:How much time will it take to reach its highest point?
How long will it stay in the air?When it returns to earth, how fast will it be moving?Answers:A: 0.71 sB: 1.4 sC: 7.0 m/s