Where does the equation s = ½ (u + v)t come from?
I m taking physics and there is a problem that uses this equation to answer it, however, no where in my book does it give the equation. Just wondering if it s just an equation that I need to know, or if there was steps that are implied that I have missed to reach this equation.
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If and only if the acceleration is constant then the AVERAGE velocity is 1/2 of the sum of the starting and ending velocities.
It means that the distance travelled by something accelerating from u to v in time t must be the same as the distance travelled by something moving at the constant speed of 1/2 (u+v)
There are many different derivations. Area under the graph, averages, and integrals are some of the processes but they all cause the same result.
From the most basic of all kinematic relationships: distance = average speed X time traveled, S = Vavg T and when V = U + AT and A = constant, we can show that Vavg = (V + U)/2.
And there we are S = Vavg T = (U + V) T/2 QED.
s is the distance. u and v are the initial and final velocities.
½ * (u + v) is the average velocity
Distance = Average velocity * time
This equation is used when the acceleration is constant. Let me give you an example.
A car has a velocity of 5 m/s. Three seconds later, the car’s velocity is 15 m/s.
s = ½ * (5 + 15) * 3 = 30 meters
Let’s use the following equation to determine the acceleration.
vf = vi + a * t
15 = 5 + a * 3
a = 3⅓ m/s^2
The following equation can also be used to determine the distance the car moves in 3 seconds.
d = vi * t + ½ * a * t^2
d = 5 * 3 + ½ * 3⅓ * 3^2 = 30 meters
Let me show one more equation that can be used to determine the distance the car moves.
vf^2 = vi^2 + 2 * a * d
15^2 = 5^2 + 2 * 3 ⅓ * d
6⅔ * d = 200
d = 200 ÷ 6 ⅔ = 30 meters
If you go to the website below, you will see these three equations. I hope this is helpful for you.
http://www.physicsclassroom.com/class/1DKin/Lesson...
It also assumes uniform acceleration
It is just based on the idea that distance = velocity * time
In this case you have a starting velocity and an ending velocity.
Think how you find the average of two values: you add them together and divide by 2.
This equation is just saying "Displacement equals average velocity multiplied by time."
Yes, it's often the "forgotten" kinematics equation. They all assume constant acceleration.
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