Chapter 2, Problem 59GP

To determine

The length of the front end of the car to collapse during the crash

Answer to Problem 59GP

1.31 m.

Explanation of Solution

Given:

Initial velocity of the car before crash $=v_i=100\frac{\text{km}}{\text{h}}=(100)\left(\frac{\text{1000 m}}{\text{3600 s}}\right)=\text{27}\text{.78}\frac{\text{m}}{\text{s}}$

Final velocity of the car after crash $=v_f=0\frac{\text{km}}{\text{h}}=0\frac{\text{m}}{\text{s}}$

Maximum acceleration of the car $=a=-30g=-30\left(9.8\frac{\text{m}}{{\text{s}}^{\text{2}}}\right)=-294\frac{\text{m}}{{\text{s}}^{\text{2}}}$

Displacement of the car during the crash = length of the front end $=x$

Formula Used:

Kinematics equation that relates final velocity, initial velocity, acceleration and displacement of an object is given as

  $v_f^2=v_i^2+2ax$

Calculation:

Substituting the values,

  $\begin{array}{l}{0}^2={27.78}^2+2(-294)x\\ 0=771.73-588x\\ x=\frac{771.73}{588}\\ x=1.31\text{m}\end{array}$

Conclusion:

Therefore, length of the front end of the car is 1.31 m.