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Mechanics IIAcceleration

Acceleration

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Acceleration• is a vector quantity defined as the

rate at which an object changes its velocity. An object is accelerating if it is changing its velocity.

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Acceleration

• The increase or decrease of velocity per unit time is called acceleration.

• It is the rate of change of velocity.• Acceleration may be

– A change in magnitude

Or

– A change in direction

Or

– Both

• Its units are meters per second squared (m/s2).

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…and some notes…

• Acceleration is a vector.

• It can be positive or negative.

• At rest means initial time is zero.

• When velocity is constant, acceleration is zero.

• When velocity increases at a constant rate, acceleration is uniform.

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Uniformly Accelerated Motion Along a Straight Line

• In this case…• acceleration is a constant

• and the acceleration vector lies in the line of the displacement vector.

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Accelerating Objects

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Acceleration

Average acceleration is the change in velocity divided by the change in time.

Acceleration = change in velocity

change in time

tv

tt

vva

if

if

av

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The 5 Acceleration Equations!

tvdav

2

) (t v vd

i f

atvvif

221 attvd

i

advvif

222

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S-t, v-t, a-t graphs for constant acceleration

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Definitions

• Instantaneous Velocity– the slope of the displacement versus time graph

• Instantaneous Acceleration– the slope of the velocity versus time graph

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SlopesD

ispl

acem

ent

Time

A

B

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Six Cases of Acceleration

1 - speed up in positive direction = positive accel.

a

+ direction

vf = 8 m/svi = 5 m/s

t = 3 seconds

fin

al

init

ial

Calculate average acceleration!

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Six Cases of Acceleration

2 - slow down in positive direction = negative accel.

a

+ direction

vi = 8 m/s vf = 5 m/s

t = 3 seconds

fin

al

init

ial

Calculate average acceleration!

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Six Cases of Acceleration

3 - speed up in negative direction = negative accel.

+ direction

vf = -8 m/s vi = -5 m/s

a

t = 3 seconds

fin

al

init

ial

Calculate average acceleration!What is happening to speed?, velocity?

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Six Cases of Acceleration4 - slow down in negative direction = positive accel.

fin

al

init

ial+ direction

vf = -5 m/s vi = -8 m/s

t = 3 seconds

Calculate average acceleration!What is happening to speed?, velocity?

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Six Cases of Acceleration

5 - reverse directions from pos to neg = negative accel.

vf = -1 m/svi = +1 m/s

a

+ direction t = 3 seconds

init

ial

fin

al

Calculate average acceleration!

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Six Cases of Acceleration

6 - reverse directions from neg to pos = positive accel.

vf = -1 m/svi = +1 m/s

a

+ direction t = 3 seconds

init

ial

fin

al

Calculate average acceleration!

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Horizontal AccelerationHorizontal Acceleration

Consider an airplane taking off. As it goes down the runway it increases its speed until it is going fast enough to “lift off” the ground.

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……but wait a minute…but wait a minute…

What if it’s vertical straight line motion…say, like a rocket going up at Cape Canaveral?!?

When you are traveling in a vertical direction, acceleration is always the same.

It is the acceleration of gravity, g, which always has the same value.

For vertical motion problems, simply substitute g for a in any of the straight-line motion equations.

2/80.9 smg

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Airborne motion isUNIFORMLY ACCELERATED MOTION

the change in velocity over time is linear so we say the change in velocity is constant

This constant acceleration is = -9.8 m/s2

This is the rate at which any airborne object will accelerate.

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Free Fall

• The force of gravity points downward– Acceleration of gravity near the surface of Earth is

called g = 9.8 m/s2 = 32.1 ft/s2

• Air resistance ignored

• We have then the conditions of one-dimensional kinematics – straight line motion with constant acceleration.

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• 6-9 Gs: "Increased chest pain and pressure; breathing difficult, with shallow respiration from position of nearly full inspiration; further reduction in peripheral vision, increased blurring, occasional tunneling, great concentration to maintain focus; occasional lacrimation; body, legs, and arms cannot be lifted at 8 G; head cannot be lifted at 9 G."

• 9-12 Gs: "Breathing difficulty severe; increased chest pain; marked fatigue; loss of peripheral vision, diminution of central acuity, lacrimation."

• 15 Gs: "Extreme difficulty in breathing and speaking; severe vise-like chest pain; loss of tactile sensation; recurrent complete loss of vision.

Human Response to Sustained g’s

Data primarily from: Bioastronautics Data Book, second edition, 1973, NASA)

In certain activities people experience + & - accelerations. By standardizing these accelerations to the normal acceleration on earth (-9.8 m/s/s) you get an idea of how much force they are experiencing

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Problem Solution

1. Draw a picture.

2. List values for any parameters that are given.

3. Find equations in which all of the variables are known except the one that you are trying to find.

4. Isolate

5. Substitute values for variable and solve.