# How long will it take cars to overtake?

## 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?

## The Attempt at a Solution

So let $t$ represent the time since the FIRST car, Car A has taken off.
Let $T$ represent the time since the SECOND car, Car B has taken off.

Note that $T = t - 6$.

$x_A(t) = (3/2)t^2$
$x_B(t) = (5/2)(t-6)^2$

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?

Orodruin
Staff Emeritus
Homework Helper
Gold Member
This is again a problem of the problem author making implicit assumptions. If someone asked me how long it would take to overtake A I would think it natural to use the time since the "chase" started, i.e., ##T##. A complete answer would include the reference time and be of the form "it would take 21 seconds after car B has started to accelerate".

On a side note, answering with five significant digits is not reasonable as your input data only has two there is no way that you could have this amount of accuracy.

ehild
Homework Helper

## 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?
The question clearly refers to the second car.

ehild

@Orodruin, then how would you find the answer? 20.6 rounded up IS 21 seconds after all . what is the solution, I think this is this closest because it it matching up the position.

bump, the answer T = 20.608 is correct because I think the test-bank rounds it off.

Orodruin
Staff Emeritus