Chapter 3.1 Chapter 3.1 NotesNotesRateRate

The The speedspeed of an object is the of an object is the ratio of distance in a given time.ratio of distance in a given time.

You can measure speed with a You can measure speed with a stop watchstop watch and a and a meter stick.meter stick.

Speed = Speed = Distance / timeDistance / time S = S = d/td/t This equation tells us the speed if This equation tells us the speed if

the speed is the speed is constantconstant

If the speed varies, If the speed varies, than we must find the than we must find the averageaverage speed. speed.

Average speed = Average speed = change in distance / change in distance / change in timechange in time

VVaveave = = d / d / tt

You leave home and drive 100 You leave home and drive 100 miles east. The trip takes 2 hours. miles east. The trip takes 2 hours. On the return trip you drive On the return trip you drive through a rainstorm and take 3 through a rainstorm and take 3 hours driving the same 100 miles.hours driving the same 100 miles.

Calculate the average speed Calculate the average speed driving to your friend’s house.driving to your friend’s house.

Calculate the average speed Calculate the average speed driving from your friend’s house.driving from your friend’s house.

Calculate the average speed for Calculate the average speed for the entire tripthe entire trip

You leave home and drive 100 You leave home and drive 100 miles east. The trip takes 2 hours. miles east. The trip takes 2 hours. On the return trip you drive On the return trip you drive through a rainstorm and take 3 through a rainstorm and take 3 hours driving the same 100 miles.hours driving the same 100 miles.

Calculate the average speed Calculate the average speed driving to your friend’s house.driving to your friend’s house.

VVaveave = = d / d / ttVVave ave = 100 miles / 2 hrs= 100 miles / 2 hrsVVave ave = = 50 miles/hr50 miles/hr

You leave home and drive 100 You leave home and drive 100 miles east. The trip takes 2 hours. miles east. The trip takes 2 hours. On the return trip you drive On the return trip you drive through a rainstorm and take 3 through a rainstorm and take 3 hours driving the same 100 miles.hours driving the same 100 miles.

Calculate the average speed Calculate the average speed driving from your friend’s house.driving from your friend’s house.

VVaveave = = d / d / ttVVave ave = 100 miles / 3 hrs= 100 miles / 3 hrsVVave ave = = 33.3 miles/hr33.3 miles/hr

You leave home and drive 100 You leave home and drive 100 miles east. The trip takes 2 hours. miles east. The trip takes 2 hours. On the return trip you drive On the return trip you drive through a rainstorm and take 3 through a rainstorm and take 3 hours driving the same 100 miles.hours driving the same 100 miles.

Calculate the average speed for Calculate the average speed for the entire tripthe entire trip

VVaveave = = d / d / ttVVave ave = 200 miles / 5 hrs= 200 miles / 5 hrsVVave ave = = 40 miles/hr40 miles/hr

The speed at any one The speed at any one instant is called the instant is called the instantaneous speedinstantaneous speed..

The instantaneous The instantaneous speed can be found speed can be found in a car with the in a car with the speedometerspeedometer..

When we state the speed When we state the speed and direction of an and direction of an object, we are stating the object, we are stating the object’s object’s VelocityVelocity..

Velocity tells us direction Velocity tells us direction and size so it is a and size so it is a vectorvector..

Speed tells us only size Speed tells us only size so it is a so it is a scalarscalar..

• If you have a car going at a If you have a car going at a constant speed and driving on a constant speed and driving on a circular path, is the velocity circular path, is the velocity constant? constant?

• Velocity depends on both speed Velocity depends on both speed and direction.and direction.

• The speed is constant.The speed is constant.• Is the direction constant (North Is the direction constant (North

only)?only)?• No – so the Velocity is not No – so the Velocity is not

constant.constant.

The vector that defines The vector that defines the distance and the distance and direction between two direction between two positions is called positions is called displacementdisplacement..

Displacement is like a Displacement is like a short cutshort cut directly from directly from one point to another.one point to another.

Average velociAverage velocity ty ==displacemedisplacement/timent/time

V = V = d/td/t

• If you have a If you have a displacement of 145 km displacement of 145 km and your flight takes 2 and your flight takes 2 hours, what is your hours, what is your average velocity?average velocity?

• v = d/tv = d/t• v = 145 km / 2 hrsv = 145 km / 2 hrs• v = v = 72.5 km/hr72.5 km/hr

The rate of change of The rate of change of an object’s velocity is an object’s velocity is the the accelerationacceleration. (How . (How fast you speed up or fast you speed up or how fast you slow how fast you slow down)down)

Acceleration is a Acceleration is a vectorvector..

Average Average acceleration = acceleration = change in change in velocity / timevelocity / time

A = (VA = (Vff – V – Vii) / t) / t

• A pilot increases the takeoff A pilot increases the takeoff speed of an airplane from 20 speed of an airplane from 20 ft/s to 200 ft/s in 30 seconds. ft/s to 200 ft/s in 30 seconds. What is the average What is the average acceleration?acceleration?

A = (VA = (Vff – V – Vii) / t) / t A = (200 ft/s – 20 ft/s) / 30 sA = (200 ft/s – 20 ft/s) / 30 s A = 180 ft/s / 30 sA = 180 ft/s / 30 s A = A = 6 ft/s6 ft/s22

Speed and velocity Speed and velocity are rates of are rates of linearlinear motion. (in a motion. (in a straight line)straight line)

Angular speedAngular speed is is a rate of rotational a rate of rotational motion.motion.

Angular speed Angular speed = = angular angular displacement/ timedisplacement/ time

w = w = θ/θ/tt Angle = Angle = # of turns # of turns

x 2pix 2pi

• If we have a tire that rotates If we have a tire that rotates 30 times in 60 seconds, what is 30 times in 60 seconds, what is the angular speed of the tire?the angular speed of the tire?

• w = w = θ/θ/tt• Θ=# of turns x 2 piΘ=# of turns x 2 pi• Θ = 30 x 2 piΘ = 30 x 2 pi• Θ = Θ = 188.4 rad188.4 rad• w = 188.4 rad / 60 sw = 188.4 rad / 60 s• w = w = 3.14 rad /s3.14 rad /s

Speed = Speed = radius radius x angular x angular speedspeed

v = v = r x wr x w

• A vacuum cleaner has a shaft A vacuum cleaner has a shaft that is 1.5 inches in diameter that is 1.5 inches in diameter and turns at an angular speed of and turns at an angular speed of 2000 rad/s, what is the speed of 2000 rad/s, what is the speed of the belt connected to this shaft?the belt connected to this shaft?

• v = r x wv = r x w• radius = diameter/2radius = diameter/2• r = 1.5 / 2 = .75r = 1.5 / 2 = .75• v = .75 in x 2000 rad/sv = .75 in x 2000 rad/s• v = v = 1500 in/s1500 in/s

Change in angular speed Change in angular speed = = angular accelerationangular acceleration

The The angular angular accelerationacceleration is the ratio is the ratio of the change in angular of the change in angular speed to the time speed to the time interval.interval.

Angular Angular acceleration = acceleration = change in change in angular speed / angular speed / timetime

α = (wα = (wff – w – wii)/t)/t

• A car’s brake is applied to a A car’s brake is applied to a wheel for 5 seconds, reducing the wheel for 5 seconds, reducing the wheel’s angular speed from 220 wheel’s angular speed from 220 rad/sec to 180 rad/sec. What is rad/sec to 180 rad/sec. What is the angular acceleration?the angular acceleration?

• α = (wα = (wff – w – wii)/t)/t• α = (180 rad/s – 220 rad/s)/5 sα = (180 rad/s – 220 rad/s)/5 s• α = -40 rad/s / 5 sα = -40 rad/s / 5 s• α = α = -8 rad/s-8 rad/s22

Position TimPosition Time Graphe Graph