# Thread: Help with Mechanics - Distance Travelled

1. ## Help with Mechanics - Distance Travelled

Hi all,

I have the following question but I'm not sure where to start?

- A particle travels, starting with initial speed u, with uniform acceleration a. Show that the distance travelled during the nth second is u+an-1/2a.

Does anyone have any idea how to do this? Any help would be greatly appreciated!

Thanks,
Ronan

2. Originally Posted by ronan116
Hi all,

I have the following question but I'm not sure where to start?

- A particle travels, starting with initial speed u, with uniform acceleration a. Show that the distance travelled during the nth second is u+an-1/2a.

Does anyone have any idea how to do this? Any help would be greatly appreciated!

Thanks,
Ronan
You should know that starting from $s=0$ the position of the particle after $t$ seconds with these assumptions is:

$
s(t)=\frac{at^2}{2}+ut
$

Then the distance moved in the $n$th second is:

$
d(n)=s(n)-s(n-1)
$

CB

3. Thanks I get the first part but how did you get from there to the second part?

4. Originally Posted by ronan116
Thanks I get the first part but how did you get from there to the second part?
At the start of the n-th second the position is s(n-1) at the end of the n-th second the position is s(n) and as the particle is always moving in the same direction the distance traveled in the n-th second is the difference of the two positions

CB

5. Ok, I get why the distance travelled would be s(n) - s(n-1) but how does that give me the equation u+an-1/2a?