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## Homework Statement

A car starts from rest and accelerates uniformly at 3.0 m/s2. A second car starts from rest 6.0 s later at the same

point and accelerates uniformly at 5.0 m/s2. How long does it take the second car to overtake the first car?

## Homework Equations

## The Attempt at a Solution

So let [itex]t[/itex] represent the time since the FIRST car,

**Car A**has taken off.

Let [itex]T[/itex] represent the time since the SECOND car,

**Car B**has taken off.

Note that [itex]T = t - 6[/itex].

[itex]x_A(t) = (3/2)t^2 [/itex]

[itex]x_B(t) = (5/2)(t-6)^2[/itex]

Let x_A(t) = x_B(t) you find,

t = 26.618,

So I say that 26.618 seconds after the first car starts, the second car overtakes it.

The correct answer is 21 seconds.

26.618 - 6 = 20.618 =~ 21.

My point is, they dont explain from which "frame of reference" you should point out your time, then why isnt t = 26.618 correct?