College Physics by Openstax Chapter 4 Problem 8

What is the deceleration of the rocket sled if it comes to rest in 1.1 s from a speed of 1000 km/h? (Such deceleration caused one test subject to black out and have temporary blindness.)

Solution:

We are given the following: v0=1000 km/hv_{0}=1000 \ \text{km/h}, vf=0 km/hv_{f}=0 \ \text{km/h}, Δt=1.1 s\Delta t = 1.1 \ \text{s}.

The acceleration is computed as the change in velocity divided by the change in time.

a=ΔvΔta=vf−voΔta=(0 km/h−1000 km/h)(1000 m1 km)(1 h3600 s)1.1 sa=−252.5 m/s2  (Answer)\begin{align*} a & = \frac{\Delta v}{\Delta t} \\ a & = \frac{v_{f}-v_{o}}{\Delta t} \\ a & = \frac{\left( 0\ \text{km/h}-1000 \ \text{km/h} \right)\left( \frac{1000 \ \text{m}}{1\ \text{km}} \right) \left( \frac{1\ \text{h}}{3600\ \text{s}} \right)}{1.1\ \text{s}} \\ a & = -252.5\ \text{m/s}^2 \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)\\ \end{align*}
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