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

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

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!

2. Originally Posted by 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!
(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.

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

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

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

3. That's not the correct answer.

4. Originally Posted by s3a
I think that's because $v_f$ is not 0. Because after the collision they slide together.

5. 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.

6. 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?