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VCE Stuff => VCE Science => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Physics => Topic started by: anjesa on March 08, 2012, 05:51:18 pm

Title: Formulas
Post by: anjesa on March 08, 2012, 05:51:18 pm: Hi, I'm just wondering why some formulas give different answers to others even though you're trying to find the same value?

For example, An American Air Force sled used by Nasa for testing human endurance under large accelerations can reach a speed of 1010km/h from rest in 2 seconds.

Calculate how far the rocket sled travels in 2 seconds.

I did x=vt so 1010/3.6 * 2 =561.2m but then the solutions say the correct formula to use is x=0.5(u+v)t.
Why is this?
Title: Re: Formulas
Post by: Lasercookie on March 08, 2012, 06:39:21 pm: The velocity in x=vt refers to average velocity ( $v_{avg}=\frac{\Delta x}{\Delta t}$ ). The value you are given (1010km/h) is not the average velocity - it is the instantaneous speed at 2 seconds.

This means we have to should take this into account. We can do this by using the average velocity. We know the there is an initial velocity and that there is a final velocity. So the average velocity would be $\frac{v+u}{2}$ . (you can also use calculus to show that $v_{avg}=\frac{\Delta x}{\Delta t}=\frac{v+u}{2}$ although the $\frac{v+u}{2}$ only applies when acceleration is constant).

So $x=vt$
$x=(\frac{v+u}{2})t$
$x=\frac{1}{2}(v+u)t$

Which is why we use that formula. You could also calculate the average velocity separately, and then use x=vt and you'll get the same answer from both formulas (after all, that's really just doing the same thing).

So $x=\frac{1}{2}(v+u)t=\frac{1}{2}(1010/3.6)*2=280.6m$

You can now also confirm that the average velocity answers are the same.
$v=\frac{v+u}{2}=\frac{1010/3.6 + 0}{2}=\frac{280.6}{2}=140.3$ and

$v=\frac{\Delta x}{\Delta t} = \frac{280.6-0}{2} = 140.3$
Title: Re: Formulas
Post by: anjesa on March 08, 2012, 07:42:22 pm: Thankyou it makes so much more sense now!