Assume that an intercontinental ballistic missile goes from rest to a suborbital speed of 6.50 km/s in 60.0 s (the actual speed and time are classified). What is its average acceleration in m/s2 and in multiples of g (9.80 m/s2) ?
Solution:
The formula for acceleration is
\overline{a}=\frac{\Delta v}{\Delta t}Substituting the given values
\begin{align*}
\overline{a} & = \frac{v_f-v_0}{\Delta t} \\
\overline{a} & =\frac{6.5\times 10^3\:\text{m/s}-0\:\text{m/s}}{60.0\:\text{sec}}\\
\overline{a} & =108.33\:\text{m/s}^2 \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)
\end{align*}This can be expressed in multiples of g
\begin{align*}
\overline{a} & = \frac{108.33\:\text{m/s}^2}{9.80\:\text{m/s}^2}\\
\overline{a} & =11.05\text{g} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)
\end{align*}Therefore, the average acceleration is 108.33 m/s2 and can be expressed as 11.05g.
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