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