physics 11 today: constant acceleration. grading scale for physics11 (it might change) 2013/2014...
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PHYSICS 11
TODAY:• Constant Acceleration
Grading Scale for Physics11 (it might change)
2013/2014
Assignments (worksheets, labs, homework, pop-quizzes)15%Quizzes (around 25 of them)20%Unit Tests (7 of them – 5% each)
35%Projects (posters, ppt presentations, research etc..) 10%Final Exam
20%
Letter Grades for Physics11 (it might change)
2013/2014A 100% – 86%B 85% – 73%C+ 72% – 67%C 66% – 60%D 59% - 50%F 49% - under
2.3 Constant (Uniform) Acceleration
2.3 Constant (Uniform) Acceleration
Motion with a Constant Acceleration
Each 0.1 second, the ball’s velocity
increases by exactly the same amount
1 second interval – so each image is taken
every 0.1 second
Motion with a Constant AccelerationTime
(s)Displacement
(m)Velocity
(m/s)Acceleration
(m/s2)
0.0 0.0 0.0 0.00.1 0.1 1.0 10.00.2 0.4 2.0 10.00.3 0.9 3.0 10.00.4 1.6 4.0 10.00.5 2.5 5.0 10.00.6 3.6 6.0 10.00.7 4.9 7.0 10.00.8 6.4 8.0 10.00.9 8.1 9.0 10.01.0 10.0 10.0 10.0
Each 0.1 second, the ball’s velocity increases
by exactly the same amount
What can you say about acceleration
when velocity is increasing by the
same amount?
Because velocity increases at each time interval,
the displacement for each time interval also increases
What can you say about displacement
when velocity is increasing by the
same amount?
Relationships between displacement, velocity and acceleration
For any object moving at constant acceleration!
Δx = displacementv0 = initial velocity
vf = final velocity
vave =
Δt = time intervala= acceleration
Average velocity - vave =
We know that the averagevelocity is equal to displacement divided by the
time interval.
vave =
For an object moving with constant acceleration,
vave =
vave =
vave = =
1. If you know initial and final velocity and time interval
vave =
½ (vf + v0)
And you want to find out DISPLACEMENT
Equation 1
Think About it…Look at the following graph of velocity vs. time. Find the area of the triangle in terms
of vf and tf
1. Compare it to the Equation 1 from the
previous slide.
What do you observe?
2. What else do you notice?
Think About it…
vf
tf
Look at the following graph of velocity vs. time. Find the area of the triangle in terms
of vf and tf ½ vf 1. The same as
Equation 1 with vi equals
to 02. The area under the line of the velocity
vs. time = displacemen
t
Problem 1A biker accelerates from 5.0 m/s to 16 m/s
in 8.0 s. Assuming uniform (constant) acceleration,
What distance does the bicyclist travel during this interval?
Problem 1
84 m
2, If you know initial velocity, time, and acceleration 1
And you want to find out FINAL VELOCITY
y = mx + by =
m = x = b =
2, If you know initial velocity, time, and acceleration 1
And you want to find out FINAL VELOCITY
y = mx + by = vf
m = ax = tb = vi
2, If you know initial velocity, time, and acceleration 1
And you want to find out FINAL VELOCITY
vf = at + v0y = vf
m = ax = tb = v0
And you want to find out FINAL VELOCITY
v0 + a
Equation 2
2, If you know initial velocity, time, and acceleration 1
The graph below shows the uniform acceleration of an
object, as it was allowed to drop off a cliff.
a. What was the acceleration of the object?
b. Write the equation for the graph
a.
b.
v0 + a
Problem 2.3.1 on page 56
Problem 2.3.1 on page 56
v0 = 15.0 m/s
slope = 4.00 m/s2
Problem 2.3.1 on page 56
acceleration
vf = 15.0 + (4.00)t
Problem 2.3.1 on page 56
5.0 m/s
9.8 m/s2
vf = 5.0 + (9.8)(1.2) = 17 m/s
3. If you know initial velocity, time, and acceleration 2
And you want to find out DISPLACEMENT
½ (vf + vi)
Equation 1
v0 + a
Equation 2
3. If you know initial velocity, time, and acceleration 2
v0 + a
And you want to find out DISPLACEMENT
½ (vf + v0)
If you know initial velocity, time, and acceleration 2
And you want to find out DISPLACEMENT
v0+ a()2
Equation 3
Think About it…Look at the following graph of velocity vs. time. Find the total area under the curve
in the terms of of v0, Δtf and a.
What do you observe?
Think About it…
vf
Δt
The total area under
the line equals to
displacement
v0
Look at the following graph of velocity vs. time. Find the total area under the curve in the terms
of of v0, Δtf and a. v0+ a()2
v0
Δv
Problem 2A plane starting from the rest at one end
of a runway undergoes a uniform acceleration of 4.8 m/s2 for 15 seconds
before take off.
Problem 21. What is its speed at take off?
2. How long must the runaway be for the plane to be able to take off?
Problem 2
72 m/s 540 m
4. If you know initial velocity, displacement and acceleration
½ (vf + v0) And you want to find out final velocity
v0 + a
And you want to find out final velocity
v0 + 2a
4. If you know initial velocity, displacement and acceleration
Equation 4
Problem 3A person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.500 m/s2. What is the velocity of the stroller after it has traveled 4.75 m?
KINEMATICS EQUATIONS
v0 + 2a
v0+ a()2
½ (vf + v0)
v0 + a
Quick Check – page 58
vf = 25.0m/sa = 3.0 m/s2
t = 5.0 svi = ??d = ∆x = no info
Equation 1
10 m/s, east
vf = 16.0 m/sa = no infot = 8.00 svi = 0.0 m/sd = ∆x = ??
Equation 2
64.0 m
Equation 4 41.6 m
2.3 Uniform Acceleration
HOMEWORKPage: 62 – 63Problems: 1, 3, 5, 7