Intro Physics Distance Travelved Question

[maff is tuff]

Homework Statement

If a car moving at 90.0 mph takes 400 ft to stop with uniform acceleration after its brakes are applied, how far will it take to stop under the same conditions if its initial velocity is 45.0 mph?

Thanks for the help :)

Homework Equations

The Attempt at a Solution

I have attached my attempt at the solution.

 

[nayfie]

Have you come across this equation?

$v^{2} = u^{2} + 2as$

 

[maff is tuff]

No but I've come across this one:

v^2=v0^2 +2a(x-x0)

Are those the same?

 

[nayfie]

Yes they're the same thing, just using different symbols and such.

Use the above formula to calculate the acceleration required to stop the car (in the first case).

The question tells you to assume the same conditions for the second case (therefore the acceleration is the same).

Once you start it should all work itself out :)

 

[maff is tuff]

Okay thanks I'll try that formula. But why didn't the formula that I used work? I solved for (x-x0) and it should have given me the right answer. And for future reference...when I reply to my own thread do you get some kind of notification or are you just checking back here? Thanks

 

[nayfie]

The source of your error appears to be this;

$400 ft = (132 \frac{ft}{s})t + \frac{1}{2}at^{2}$ (Line 1 - Correct)

$400 ft = 132 ft + \frac{1}{2}at^{2}$ (Line 2 - Incorrect)

The equation you were using;

$x - x_{0}= v_{0}t + \frac{1}{2}at^{2}$

You then changed it to;

$x - x_{0} = x + \frac{1}{2}at^{2}$ (No longer the same formula - you can't cancel the per second and the variable t.)

All working after that will then be invalid.

I just attempted to solve the problem using your method, but am left with a variable of time which we have no way of getting without the acceleration. I attached a photo of my workings using your method in case you're interested. (I'm from Australia so I converted the units to metres and metres per second)

If you need any more help let me know. :)

P.s Whenever somebody replies to a thread I've posted in, I am sent an e-mail. I can check my e-mails from my phone.

 

[maff is tuff]

Ok I see my dumb mistake now. I don't know why but I canceled the seconds out with the time. But now I see that time is not just seconds because for all we know it can be an interval so I can't just cancel out the "t" with the "s". Ok I'm going to go ahead and try the other formula you suggested. Thanks again for the detailed explanation; I probably would have never seen that horrible mistake.

 

[nayfie]

No worries mate! We all make mistakes. It was a good attempt though!