In the real world, objects move with changing In the real world, objects move with changing velocities. A new concept called velocities. A new concept called accelerationacceleration

has been defined to describe how velocity has been defined to describe how velocity changes. changes. AccelerationAcceleration is change in is change in velocity velocity withwith

respect respect toto time. Velocity time. Velocity can change in three can change in three ways: ways: (a) (a) change in speed, either change in speed, either increaseincrease or or

decreasedecrease; ; (b) (b) change in direction; and change in direction; and (c) (c) change in speed as well as direction. Thus , an change in speed as well as direction. Thus , an object is said to be accelerating when it either object is said to be accelerating when it either

moving with changing speed, moving with moving with changing speed, moving with constant speed but with changing direction, or constant speed but with changing direction, or

moving with changing speed as well as moving with changing speed as well as changing direction. changing direction.

acceleration = change in velocityacceleration = change in velocity time time

a= ∆a= ∆vv ∆t ∆t

Since acceleration is defined in Since acceleration is defined in terms of velocity, it is also a vector quantity. terms of velocity, it is also a vector quantity.

The SI unit of acceleration is meter per second The SI unit of acceleration is meter per second per second, m/s/s or m/sper second, m/s/s or m/s2.2.

Changes in Changes in SpeedSpeed

Falling objects Falling objects accelerate in response accelerate in response to the force exerted on to the force exerted on them by Earth’s gravity. them by Earth’s gravity.

Different objects Different objects accelerate at the same accelerate at the same rate, regardless of their rate, regardless of their mass. This illustration mass. This illustration

shows the speed at shows the speed at which a ball and a cat which a ball and a cat would be moving and would be moving and

the distance each would the distance each would have fallen at intervals have fallen at intervals of a tenth of a second of a tenth of a second

during a short fall.during a short fall.

Changes in Changes in DirectionDirection

When a ball is whirled When a ball is whirled in a circle, it is in a circle, it is

accelerating accelerating inwardinward. . This inward This inward

acceleration is caused acceleration is caused by a by a centripetalcentripetal, or , or

center-seeking, force center-seeking, force supplied by the tension supplied by the tension

in the string. The in the string. The required force is equal required force is equal

to to mvmv22//rr, where , where mm is is the mass of the ball, the mass of the ball, vv is its velocity (speed is its velocity (speed

and direction), and and direction), and rr is is its distance from the its distance from the center of revolutioncenter of revolution..

Change in VelocityChange in Velocity

Each time you take a Each time you take a step you are changing step you are changing the velocity of your body.the velocity of your body.

You are probably most You are probably most familiar with the velocity familiar with the velocity changes of a moving bus changes of a moving bus or car.or car.

The rate at which The rate at which velocity (speed or velocity (speed or direction) changes occur direction) changes occur is called acceleration.is called acceleration.

Changes in both Speed and Changes in both Speed and DirectionDirection

Acceleration often involves both a change in speed Acceleration often involves both a change in speed and a change in direction. Changing both components and a change in direction. Changing both components of velocity results in a curved path of motion. In these of velocity results in a curved path of motion. In these cases, the acceleration vector is the sum of two parts cases, the acceleration vector is the sum of two parts (components). One part, the tangential acceleration, (components). One part, the tangential acceleration,

acts along the direction of motion, parallel to the acts along the direction of motion, parallel to the velocity, resulting in a change of speed. The other velocity, resulting in a change of speed. The other

part, the radial acceleration, acts perpendicular to the part, the radial acceleration, acts perpendicular to the direction of motion, resulting in a change of direction. direction of motion, resulting in a change of direction. In order to change the speed of an object moving in a In order to change the speed of an object moving in a

circle, for example, one needs some acceleration circle, for example, one needs some acceleration along the direction of motion, in addition to the along the direction of motion, in addition to the

component of acceleration in the radial direction component of acceleration in the radial direction (pointing to the center) that keeps the object moving (pointing to the center) that keeps the object moving in a circle. In the case of a space shuttle in orbit, the in a circle. In the case of a space shuttle in orbit, the radial acceleration is the force of gravity pulling the radial acceleration is the force of gravity pulling the shuttle toward Earth, while a tangential acceleration shuttle toward Earth, while a tangential acceleration

is achieved by firing rockets along the direction of is achieved by firing rockets along the direction of motion.motion.

Acceleration= Acceleration= final velocity- starting final velocity- starting velocityvelocity

timetime

Change in velocity = final Change in velocity = final – – starting starting

velocity velocity velocity velocity

Acceleration= Acceleration= change in velocitychange in velocity

timetime

Acceleration =Velocity(final) - Velocity(original)

time

A car traveling at 60 mph accelerates to90 mph in 3 seconds. What is thecar’s acceleration?

=90 mph - 60 mph

3 seconds

=30 mph

3 seconds

= 10 mph/second

PositivePositive acceleration acceleration

Negative Negative accelerationacceleration

Acceleration =Velocity(final) - Velocity(original)

time

A car traveling at 60 mph slams on the breaks to avoid hitting a deer. The car comes to a safe stop 6 seconds after applying the breaks. What is thecar’s acceleration?

=0 mph - 60 mph

6 seconds

=- 60 mph

6 seconds

= - 10 miles per hour per second

- A constant - A constant acceleration produces acceleration produces

a straight line or linear a straight line or linear slope (rise/run). slope (rise/run).

- The slope of a non-- The slope of a non-linear velocity-time linear velocity-time graph (rise/run) will graph (rise/run) will predict an objects predict an objects

instantaneous instantaneous acceleration. acceleration.

a = v/ta = v/t

GalileoGalileo

1600’s 1600’s Studied how things Studied how things

fellfell Didn’t have a good Didn’t have a good

clockclock Rolled balls down an Rolled balls down an

inclined planeinclined plane Found that the speed Found that the speed

increased as it rolled increased as it rolled down the rampdown the ramp

GalileoGalileo

t = 0t = 1 second

t = 2 seconds

t = 3 seconds

Acceleration= Acceleration= change in change in velocityvelocity

timetime

GalileoGalileo

Same things happen when Same things happen when things fallthings fall Didn’t drop things from Tower of Pisa

vv22finalfinal = 2gd = 2gdyy

A final velocity can be A final velocity can be calculated over a vertical calculated over a vertical displacement “ddisplacement “dyy" during free " during free fall using the equation:fall using the equation:

ddyy = 1/2 gt = 1/2 gt22

The vertical displacement “dThe vertical displacement “dyy" that " that occurs during a specific time of free occurs during a specific time of free fall can be determined using the fall can be determined using the equation:equation:

Or a time interval can also Or a time interval can also be determined over a be determined over a specified distance of freefall specified distance of freefall using the equation:using the equation:

tt2 2 = 2d= 2dyy /g /g

FallingFalling Air resistance will Air resistance will

increase as it falls increase as it falls fasterfaster

An upward force on An upward force on the objectthe object

Eventually gravity Eventually gravity will balance with air will balance with air resistanceresistance

Reaches terminal Reaches terminal velocity - highest velocity - highest speed reached by a speed reached by a falling object.falling object.

Terminal velocityTerminal velocity Force of gravity is Force of gravity is

constantconstant air resistance increases as you speed up until the force is equal

Equal forces, no acceleration constant velocity terminal velocity

THE END! THE END!