# How long will it take cars to overtake?

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1. Sep 27, 2014

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

3. 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?

2. Sep 27, 2014

### Orodruin

Staff Emeritus
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.

3. Sep 27, 2014

### ehild

The question clearly refers to the second car.

ehild

4. Sep 27, 2014

@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.

5. Sep 28, 2014

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

6. Sep 28, 2014

### Orodruin

Staff Emeritus
20.608 s is what you get when you simply inserts the numbers. However, it is not reasonable to respond with five significant digits when your input data has two. Most likely you cannot make the prediction to that level of accuracy or measure the time that accurately. Using the same number of significant digits (in this case rounding to two significant digits) gives a good first order approximation of how accurate you can be. You could also answer 20.608 s and give an estimate of the error, which will be significantly larger than 0.01 s, which means that the later digits do not contain any useful information. I would therefore answer along the lines "After the second car has started, it takes about 21 s for it to catch up."

7. Sep 28, 2014

Thanks, the testmaker is just like this. It always rounds off the answer to the nearest one, no decimals. But, do you think that will be considered correct? Because if we didnt know to round it off?