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 $t$.

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