# Finding the distance in an acceleration problem?

## 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?

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.

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

How did you get that?

Now I just confused 2 questions together. Forget this whole thing, it's a flop. =(

Ok, this is what I did.
$$1km/h^{2}=1000m/(3600s)^{2}$$
Try and see what you get.

Oh, so I have to square the seconds in the speed part?

of course!

Now I got -0.1296..
Kinda on the right track.

I did -0.006/(0.36^2)

nope, still wrong. 1/3600 is not equal to 0.36.

Is this considered partially right?
0.006km/3600 seconds?

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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