Chapter 9, Problem 37P

A biomedical engineer measures the velocity profiles of a belted and unbelted occupant during a 45 mph $\left(\approx 20\text{m/s}\right)$ frontal collision, as shown in Fig. P9.37.

(a) Knowing that $x\left(t\right)=x\left(0\right)+{\displaystyle \underset{0}{\overset{t}{\int }}v\left(t\right)dt}$, find and plot the displacement $x\left(t\right)$ of the belted occupant for time 0 to 40 $ms$. Assume that the initial displacement at $t=0$ is 0 m (i.e., $x\left(0\right)=0\text{m}$ ).

(b) Find and plot the displacement $x\left(t\right)$ of the unbelted occupant for time 0 to 44 $ms$. Assume $x\left(0\right)=0\text{m}$.

(c) Based on the results of parts (a) and (b), how much farther did the unbelted occupant travel compared to the belted occupant?