Finding the distance in an acceleration problem?

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To determine the stopping distance of a car traveling at 90 km/h with an acceleration of -6.0 m/s², the correct approach involves using the formula d = (v1 + v2)/2 * t. The initial speed should be converted correctly, ensuring that units are consistent, particularly when converting acceleration from m/s² to km/h². A common mistake in the discussion was the incorrect conversion of units, which led to confusion in calculating time and distance. Ultimately, the correct stopping distance is approximately 41 meters when calculations are performed accurately. Understanding unit conversions is crucial for solving acceleration problems effectively.
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Homework Statement


What distance is required to stop a car going 90km/h if the car can stop with an acceleration of -6.0m/s2?


Homework Equations


a = v2-v1/t
d = (v1+v2/2)t


The Attempt at a Solution


I'm thinking first we have to solve for t. Which would be the speed divided by acceleration, which is -0.36 km/h^2 over 80km/h which is 0.0045 hours.

Now to solve for distance, it would be 80km/2 x 0.0045

Which leaves me with 0.18 which is completely wrong because the answer is supposed to be 41 m.

Help please? Thank you.
 
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Oops speed over acceleration is actually 80km/h over -0.36km/h, but that still gives me the wrong answer..
 
Check your equation for D again.
 
It's right ?

D = (V1 + v2/2) x T
 
1. Is it 90 or 80 km/h?
2. your formula should be \Delta d=\frac{v_{1}+v_{2}}{2}\Delta t
 
It says 80km on my sheet.
But yeah, that is the formula I am using.
(I do v1+v2 first, and then divide it by 2)
 
I think I see your mistake. How did you convert m/s^{2} to km/h^{2}
 
Oh sorry for writing 90 in the first post, that was a typo. Should be 80km.

Okay so it's 80km/h.
I converted that -5.0m/s into km/^s by doing this:

-5/1000
= - 0.005

Then I multiplied this by 60..

But now I'm getting -0.3. x_x
Ahh, can anyone thoroughly help me? This is so frustrating! I am so lost. =(
 
Ok, I think the only mistake you made was this conversion. It's acceleration, therefore has a unit of either m/s^{2} or km/h^{2}, notice the square in the bottom. I tried converting it and got 1m/s^{2}=12960km/h^{2}
 
  • #10
How did you get that?
 
  • #11
Now I just confused 2 questions together. Forget this whole thing, it's a flop. =(
I'll ask my teacher.
 
  • #12
Ok, this is what I did.
1km/h^{2}=1000m/(3600s)^{2}
Try and see what you get.
 
  • #13
Oh, so I have to square the seconds in the speed part?
 
  • #14
of course!
 
  • #15
Now I got -0.1296..
Kinda on the right track.

I did -0.006/(0.36^2)
 
  • #16
nope, still wrong. 1/3600 is not equal to 0.36.
 
  • #17
Is this considered partially right?
0.006km/3600 seconds?
 
  • #18
You really need to work on unit conversion. Let me show you:
1km/h^{2}=1000m/(3600s)^{2} 1km is replaced by 1000m, and 1h is replace by 3600s.
1km/h^{2}=1000m/(3600^{2}s^{2}) notice that both the 3600 and s are squared.

1km/h^{2}=\frac{1000}{3600^{2}}\frac{m}{s^{2}} separate the unit from the numbers.

1km/h^{2}=\frac{1}{12960}\frac{m}{s^{2}}

12960km/h^{2}=1\frac{m}{s^{2}}

Right?
 
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