Average Velocity & Average Acceleration
From High School Online Collaborative Writing
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[edit] Average Velocity
The actual definition of the term is the total distance covered divided by the total time elapsed while traveling in a given direction meaning Displacement / Time . displacement divided by time interval during which the displacement occured.
Now to put it into context suppose you're cruising south down the highway and you go 60 miles in 1 hour. Then your average velocity is 60 mi/hr south. Now say you measure everything along a line from point. That is you were driving along a straight road and you had set your odometer to zero. Now it reads 15 miles, and you look at your clock and it says that it's 9 A.M. Your initial position equals 15 miles. Later on you look at the odometer and it reads 75 miles, and your clock reads 11 AM. So we can introduce two other sets of variables to describe this. Our final position equals 75 miles, and our final time equals 11 hours. There is no point to go to all that trouble of inventing four variable names. It seems like a pretentious way of saying something quite simple. So now we are in a position to define the average velocity in one dimension. It is the ratio of the change in position, to the change in time. Hence,
The initial and final positions are measured with distance units such as miles and meters.
The intial and final times are measured with time units such as seconds, minutes and hours
Average Velocity= Final position – Initial position divided by the Final time – Initial time
So to put in the values would be (75-15)/(11-9)= 60/2=30
Hence the average velocity is 30 miles per hour.
http://www.zive.sk/Files/Obrazky/Oddych/PS/F13.jpg
[edit] Average Acceleration
Average acceleration is the rate at which velocity changes. Average acceleration is the change in velocity divided by an elapsed time. For instance, if the velocity of a marble increases from 0 to 60 cm/s in 3 seconds, its average acceleration would be 20 cm/s/s. This means that the marble’s velocity will increase by 20 cm/s every second.
The formula that we would use would be change in velocity divided by change in time. Another way to put it would be Vf-Vi/Tf-Ti. That means the final velocity is subtracted from the intial velocity and then divided by the final time subtracted by the intial time. After all that is done the value is the average velocity.
Now for example lets say If a plane moves from 20 m/s to 2000 m/s in 5 seconds, what is the car's average acceleration? By using the formula we would get 2000m /s as our final velocity and 20 m/s. The intial time would be 0 seconds as the object (in this case being the plane) and the final time would be 5 seconds. Hence by using the formula we would get
(2000-20)/(5-0)= 1980/5= 396 m/s
396 m/s would be the average acceleration of the plane.
[edit] Formulas
V(average)= Df-D1/t
a(average)=Vf-Vi/tf-ti
Vf= Vi+ a.t
d= Vi.t+ .5a.t^2
Vf^2= Vi^2+ 2.a.d
V(average)= average velocity
Vf= final velocity
Vi= intial velocity
a(average)= Average acceleration
a= acceleration
t= time
Df= final displacement
Di= initial displacement
t=time
[edit] Regents questions
An object that is originally moving at a speed of 20m/s accelerates uniformly for 5 seconds to a final speed of 50m/s. What is the acceleration of the object?
A car travels 90. meters due north in 15 seconds. Then the car turns around and travels 40. meters due south in 5.0 seconds. What is the magnitude of the average velocity of the car during this 20.-second interv
[edit] Recources and References
http://library.thinkquest.org/10796/ch3/ch3.htm
http://www.mansfieldct.org/Schools/MMS/staff/hand/lawsaveaccel2003.htm
barrons regents book
