Motion Equations for Constant Acceleration in One Dimension

A rocket accelerates at a rate of \(20 \mathrm{~m} / \mathrm{s}^{2}\) during launch. How long does it take the rocket to reach a velocity of \(400 \mathrm{~m} / \mathrm{s}?\)

Solution

To answer this, choose an equation that allows you to solve for time \(t\), given only \(a, v_{0}\), and \(v\).

\(v=v_{0}+a t\)

Rearrange to solve for \(t\).

\(t=\frac{v-v_{0}}{a}=\frac{400 \mathrm{~m} / \mathrm{s}-0 \mathrm{~m} / \mathrm{s}}{20 \mathrm{~m} / \mathrm{s}^{2}}=20 \mathrm{~s}\)