Motion & Forces Describing Motion Acceleration.

Motion & ForcesMotion & Forces

Describing MotionDescribing Motion AccelerationAcceleration

Speed & VelocitySpeed & Velocity

SpeedSpeed raterate of motion of motion distance traveled per unit timedistance traveled per unit time

time

distancespeed

vd

t

Speed & VelocitySpeed & Velocity

Instantaneous SpeedInstantaneous Speed speedspeed at a given instant at a given instant

Average SpeedAverage Speed

time total

distance totalspeed avg.

Speed & VelocitySpeed & Velocity

VelocityVelocity speed in a given speed in a given directiondirection can change even when the speed is can change even when the speed is

constant!constant!

Acceleration, Speed and Acceleration, Speed and Velocity Velocity

AccelerationAcceleration is the rate of change of is the rate of change of velocity. When the velocity of an object velocity. When the velocity of an object changes, the object is accelerating. changes, the object is accelerating.

A change in velocity can be either a A change in velocity can be either a change in change in speedspeed something is moving, or something is moving, or a change in the direction it is moving. a change in the direction it is moving.

Acceleration occurs when an object Acceleration occurs when an object changes its speed, it's direction, or changes its speed, it's direction, or bothboth. .

Acceleration, Speed and Acceleration, Speed and Velocity Velocity

When you think of acceleration, you When you think of acceleration, you probably think of something probably think of something speeding up. However, an object speeding up. However, an object that is that is slowingslowing down also is down also is accelerating.accelerating.

Acceleration also has Acceleration also has directiondirection, just , just as velocity doesas velocity does

AccelerationAcceleration

• If the acceleration is in the same If the acceleration is in the same direction as the velocity, the speed direction as the velocity, the speed increases and the acceleration is increases and the acceleration is positivepositive..

AccelerationAcceleration

If the speed decreases, the If the speed decreases, the acceleration is in the opposite acceleration is in the opposite direction from the velocity, and the direction from the velocity, and the acceleration is acceleration is negativenegative. .

Changing DirectionChanging Direction

A change in velocity can be either a A change in velocity can be either a change in how change in how fastfast something is something is moving or a change in the direction moving or a change in the direction of movement.of movement.

Any time a moving object changes Any time a moving object changes direction, its velocity changes and it direction, its velocity changes and it is is acceleratingaccelerating. .

Changing DirectionChanging Direction

The speed of the The speed of the horses in this horses in this carousel is carousel is constant, but the constant, but the horses are horses are acceleratingaccelerating because their because their direction is direction is changing changing constantly.constantly.

Calculating AccelerationCalculating Acceleration

To calculate the acceleration of an To calculate the acceleration of an object, the change in velocity is object, the change in velocity is divideddivided by the length of time interval by the length of time interval over which the change occurred.over which the change occurred.

To calculate the change in velocity, To calculate the change in velocity, subtract the subtract the initialinitial velocity—the velocity—the velocity at the beginning of the time velocity at the beginning of the time interval—from the interval—from the finalfinal velocity—the velocity—the velocity at the end of the time interval.velocity at the end of the time interval.

Calculating AccelerationCalculating Acceleration

Then the change in velocity is:Then the change in velocity is:

AccelerationAcceleration

AccelerationAcceleration the the raterate of change of velocity of change of velocity change in change in speedspeed oror directiondirection

t

vva if

a: acceleration

vf: final velocity

vi: initial velocity

t: time

a

vf - vi

t

AccelerationAcceleration

Positive accelerationPositive acceleration ““speeding speeding upup””

Negative accelerationNegative acceleration ““slowing downslowing down””

CalculationsCalculations A roller coaster starts down a hill at 10 m/s. A roller coaster starts down a hill at 10 m/s.

Three seconds later, its speed is 32 m/s. Three seconds later, its speed is 32 m/s. What is the roller coaster’s acceleration?What is the roller coaster’s acceleration?

GIVEN:

vi = 10 m/s

t = 3 s

vf = 32 m/s

a = ?

WORK:a = (vf - vi) ÷ t

a = (32m/s - 10m/s) ÷ (3s)

a = 22 m/s ÷ 3 s

a = 7.3 m/s2a

vf - vi

t

CalculationsCalculations     A skater goes from a standstill to a A skater goes from a standstill to a

speed of 6.7 m/s in 12 seconds.  What speed of 6.7 m/s in 12 seconds.  What is the acceleration of the skater?is the acceleration of the skater?

GIVEN:

vi = 0 m/s

t = 12 s

vf = 6.7 m/s

a = ?

WORK:a = (vf - vi) ÷ t

a = (6.7m/s - 0m/s) ÷ (12s)

a = 6.7 m/s ÷ 12 s

a = .56 m/s2a

vf - vi

t

CalculationsCalculationsAs a shuttle bus comes to a normal stop, it As a shuttle bus comes to a normal stop, it

slows from 9.00m/s to 0.00m/s in 5.00s. slows from 9.00m/s to 0.00m/s in 5.00s.  Find the average acceleration of the bus Find the average acceleration of the bus..

          GIVEN:

vi = 9 m/s

t = 5 s

vf = 0 m/s

a = ?

WORK:

a = (vf - vi) ÷ t

a = (0m/s - 9m/s) ÷ (5s)

a = -9 m/s ÷ 5 s

a = -1.8 m/s2

a

vf - vi

t

CalculationsCalculationsHow long will it take a car traveling

30 m/s to come to a stop if its acceleration is -3 m/s2?

GIVEN:t = ? vi = 30 m/s

vf = 0 m/s

a = -3 m/s2

WORK:t = (vf - vi) ÷ a

t = (0m/s-30m/s)÷(-3m/s2)

t = -30 m/s ÷ -3m/s2

t = 10 sa

vf -vi t

Amusement Park Amusement Park AccelerationAcceleration

Engineers use the laws Engineers use the laws of of physicsphysics to design to design amusement park rides amusement park rides that are thrilling, but that are thrilling, but harmless.harmless.

The highest speeds The highest speeds and and accelerationsaccelerations usually are produced usually are produced on steel roller on steel roller coasterscoasters..

Amusement Park Amusement Park AccelerationAcceleration

Steel roller coasters can offer Steel roller coasters can offer multiple steep drops and multiple steep drops and inversioninversion loops, which give the rider large loops, which give the rider large accelerations.accelerations.

As the rider moves down a steep hill As the rider moves down a steep hill or an inversion loop, he or she will or an inversion loop, he or she will accelerate toward the ground due to accelerate toward the ground due to gravitygravity..

Amusement Park Amusement Park AccelerationAcceleration

When riders go around a sharp turn, When riders go around a sharp turn, they also are they also are acceleratedaccelerated..

This acceleration makes them feel as This acceleration makes them feel as if a if a forceforce is pushing them toward the is pushing them toward the side of the car.side of the car.