# Can someone help me with this collision mechanics problem please?

#### s3a

Here is the question:
You are the juror of a case in - Anonymous - fLw7zWYD - Pastebin.com

I get (a) 43.67m/s but for (b) I am completely thrown off by the instantaneous acceleration. I've been trying to do (b) for like a week so it would be greatly appreciated if someone could show me their work.

Any help would be GREATLY appreciated!

#### DrDank

Here is the question:
You are the juror of a case in - Anonymous - fLw7zWYD - Pastebin.com

I get (a) 43.67m/s but for (b) I am completely thrown off by the instantaneous acceleration. I've been trying to do (b) for like a week so it would be greatly appreciated if someone could show me their work.

Any help would be GREATLY appreciated!
(b) Estimate the instantaneous acceleration of the sports car during the actual collision if the colliding cars reach the same final speed after collapsing a combined total distance of 1.0 m.

$$\displaystyle v_f^2-v_o^2=2a\Delta x$$

$$\displaystyle a=\frac{v_f^2-v_o^2}{2\Delta x}$$

$$\displaystyle a=\frac{(43.67)^2-(0)^2}{2(1)}$$

• s3a

#### DrDank

I think that's because $$\displaystyle v_f$$ is not 0. Because after the collision they slide together.

• s3a

#### s3a

Thanks! I'll try to over-analyze this problem later because my head is pounding at the moment but instead of 0 the velocity of when they are collide is 13.93m/s so I did (43.67^2 - 13.93^2)/(2*1) m/s^2 which is the right answer.

Edit: Ok so I re-analyzed the problem and it seems to me that we're trying to get as small an interval as possible for final and initial velocities (like the question states "Estimate ... ") and we're using kinematics to calculate that acceleration. Last edited:

#### s3a

Wait isn't it supposed to be:
a = (13.93^2 - 43.67^2)/(2*1) ?

I know the magnitude of the answer is the same but the internet thing that my teacher has set up said the positive one is right. Is it just because it was asking for magnitude or because, the acceleration is supposed to be positive?

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