A car starts from rest and accelerates uniformly at 3m/s2. A second car starts from rest 6 s later and accelerates uniformly at 5 m/s2/ How long does it take the second car to overtake the first car?

I feel like I know how I am supposed to do this but I just need some clarity on what formula I need to use and what all my variables are. I have been physiced out so I just need a lil help here!!!!! Thanks so much to any and all who wanna contribute!!!!!!!

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#### FZ+

Use s = ut + 1/2 *at^2, remembering to account for the "lead" the first car has acheived.

Hmm... there does seem to be a lot of uniform acceleration questions around recently...

Last edited:

#### HallsofIvy

Homework Helper
Slight typo: it should be s= (1/2)at2+ ut (u is the initial speed) instead of "2at2" (i.e. 1/2 instead of 2)

Taking the time the first car starts as t= 0, the distance the first car has gone is s1= (3/2)t2 (a= 3 and u=0 {"starts from rest"})

Car 2 also starts from rest but has a= 5 and starts 6 seconds later (so it's "time" is t- 6 rather than t).
s2= (5/2)(t- 6)2.

The second car will "overtake" the first car when they have both gone the same distance: solve (3/2)t2= (5/2)(t- 6)2.

but wait, I still am a lil confused. I guess a lot confused. that is the formula I guessed but where do I plug everything in?

okie

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