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?
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?