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This must be a relative simple question, but the answer I am obtaining doesn't appear to be logical.

Say a vehicle has a velocity of 15 m/s and an effective mass of 1000 kg including occupants. 1) What is the vehicle kinetic energy? $E_{\mathsf{kin}} =\tfrac{1}{2}mv^2 = \tfrac{1}{2} 1000\cdot 15^2 = 112500$kJ <= Here I compute the kinetic energy

Now assume the vehicle front behaves like a linear elastic spring of 225,000 N/m without energy dissipation 2) What is the peak front deformation? Potential energy = Kinetic energy, $112,500,000 = 0.5 k x^2$ with $k = 225,000$. Then $x = \sqrt{1000} = 31.6$m.

But a front deformation of $31.6$m looks very large to me, is this calculation correct?

And another question is how to calculate now the peak acceleration when the car is bumping back?

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    $\begingroup$ The Ek should be in Joules not kilo-Joules. $\endgroup$ – lemon Jun 6 '15 at 9:25
  • $\begingroup$ You were right to check that answers obtained are "sensible" - and this one was not. @lemon is right about the source of your error; and for peak acceleration, calculate the force of the spring at the time of maximum deformation. Then use &F=m\cdot a$. $\endgroup$ – Floris Jun 6 '15 at 10:52
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The kinetic energy you calculated is in joules, not kilojoules. So x is 1.0m. You can calculate the peak acceleration using the elastic force: F=kx=ma; a=kx/m

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