Calculating Overtaking Time for Two Cars Accelerating Uniformly

[LadyLexa]

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 want to contribute!

 

[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...

 

[HallsofIvy]

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.

 

[LadyLexa]

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?

 

[LadyLexa]

okie