College Physics by Openstax Chapter 2 Problem 17

Dr. John Paul Stapp was U.S. Air Force officer who studied the effects of extreme deceleration on the human body. On December 10, 1954, Stapp rode a rocket sled, accelerating from rest to a top speed of 282 m/s (1015 km/h) in 5.00 s, and was brought jarringly back to rest in only 1.40 s! Calculate his

(a) acceleration and

(b) deceleration.

Express each in multiples of g (9.80 m/s2) by taking its ratio to the acceleration of gravity.

Solution:

Part A

The formula for acceleration is

a‾=ΔvΔta‾=vf−v0tf−t0\begin{align*} \overline{a} & =\frac{\Delta v}{\Delta t} \\ \overline{a} & = \frac{v_f-v_0}{t_f-t_0} \\ \end{align*}

Substituting the given values

a‾=282 m/s−0 m/s5.00 sec⁡a‾=56.4 m/s2  (Answer)\begin{align*} \overline{a} & =\frac{282\:\text{m/s}-0\:\text{m/s}}{5.00\:\sec } \\ \overline{a} & =56.4\:\text{m/s}^2 \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right) \end{align*}

Part B

The deceleration is 

a‾=0 m/s−282 m/s1.40 sa‾=−201.43 m/s2  (Answer)\begin{align*} \overline{a} & =\frac{0\:\text{m/s}-282\:\text{m/s}}{1.40\:\text{s}} \\ \overline{a} & =-201.43\:\text{m/s}^2 \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right) \end{align*}

In expressing the computed values in terms of g, we just divide them by 9.80.

The acceleration is

a‾=56.49.80=5.76g  (Answer)\overline{a}=\frac{56.4}{9.80}=5.76\text{g} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)

The deceleration is

a‾=201.439.80=20.55g  (Answer)\overline{a}=\frac{201.43}{9.80}=20.55\text{g} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)
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