Need help with Maths/Physics problem! Can't solve it!

If someone could please help me solve this problem I'd be forever indebted! It's probably very easy, but I nor nobody else in my physics class can seem to come up with the correct answer. I'm guessing it involves calculus, so I figure its a question for someone with a knowledge of maths! Anyway, here it is:

A body passes point A and moves in a straight line with a constant velocity of 40m/s. Ten seconds after the first body passed A, another body which is at rest at A is given an acceleration of 2m/s/s and moves in the same direction as the first body. How long does it take for the second body to catch up to the first? How far from A does this occur?

Just for reference the right answers are: 48.28 seconds, and 2331.2 metres.

Could someone please explain how to do it! Thanks!

Cokehead Mother

Ten seconds after the first body passed A, its displacement is (40)(10) = 400.

The two bodies will meet when their displacements from A are equal. We're going to say t = 0 10 seconds after the first body passes A.

First body

u = 40
v= 40
a = 0
s = s - 400 (because it's already done 400m so it'll only have to move (s - 400)m in the time it takes the other body to catch up (t)
t = t

Second body

u = 0
v = v
a = 2
s = s
t = t

So we're gonna use the formula s = ut + 1/2 at^2.

First body: s - 400 = 40t.

Second body: s = 1/2 (2) t^2

Can you finish from here?

Hey, thanks for your reply! Well i've tried solving it, even carrying on from whaty you said, and I don't know what on earth I'm doing wrong but I can't manage to get the same answer as what the book says is correct.

I've tried it a few ways and I keep getting the time to be in the region of 20 seconds, but the book says its 48.28.

I know I'm probably doing something stupidly wrong, and the correct way is probably blatently obvious, but I can't see it!

Anyway you could elaborate a bit more and may try it yourself to see if you get the correct answer?

Thanks.

Cokehead Mother

s - 400 = 40t
s = 40t + 400

s = t^2
40t + 400 = t^2
t^2 - 40t - 400 = 0

t = 40/2 +/- sqrt[(-40)^2 - 4(-400)]/2 = 48.28 or -8.28 and obviously we can ignore -8.28

s = 40(48.28) + 400 = 2331.2

I see where I was going wrong now, I never thought of using the formula -b+/- etc. for finding the roots of the equation, I was just trying to find them from factors! Can't believe I didn't think of that! Thanks a million for your help anyway, much appreciated!