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### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# 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 ($${\bf{9}}{\bf{.80}}\;{\bf{m/}}{{\bf{s}}^{\bf{2}}}$$)?

The acceleration of missile is $${\bf{108}}{\bf{.33}}\;{\bf{m/}}{{\bf{s}}^{\bf{2}}}$$ or $${\bf{11}}{\bf{.05}}\,{\bf{g}}$$.

See the step by step solution

## Determination of formula for average acceleration of missile

Given data:

The suborbital speed of missile is $$v = 6.50\;{\rm{km}}/{\rm{s}}$$.

The initial speed of rocket is $$u = 0$$.

The time for acceleration of the missile is $$t = 60\;{\rm{s}}$$.

The acceleration of the missile is the increase in speed over time while moving from one position to another position.

The average acceleration of the missile is given by

$$a = \frac{{v - u}}{t}$$

Here, $$a$$ is the acceleration of missile.

## Determination of average acceleration of missile

Substitute all the values in the above equation.

$$\begin{array}{l}a = \frac{{\left( {6.50\;{\rm{km}}/{\rm{s}} - 0} \right)\left( {\frac{{1000\;{\rm{m}}}}{{1\;{\rm{km}}}}} \right)}}{{60\;{\rm{s}}}}\\a = 108.33\;{\rm{m}}/{{\rm{s}}^2}\\a = \left( {108.33\;{\rm{m}}/{{\rm{s}}^2}} \right)\left( {\frac{g}{{9.80\;{\rm{m}}/{{\rm{s}}^2}}}} \right)\\a = 11.05g\end{array}$$

Therefore, the acceleration of the missile is $$108.33\;{\rm{m}}/{{\rm{s}}^2}$$ or $$11.05\,{\rm{g}}$$.