Question

A rocket traveling at 80 m/s is accelerated uniformly to 152 m/s over a 18 s interval. What is its displacement during this time?

Answer 1

Recall that with constant acceleration,

$x_f-x_i=\dfrac{v_i+v_f}2t$

where $x_f-x_i$ is the rocket's displacment, $v_i$ is its initial velocity, $v_f$ its final velocity, and $t$ is time. So

$x_f-x_i=\dfrac{80\frac{\mathrm m}{\mathrm s}+152\,\frac{\mathrm m}{\mathrm s}}2(18\,\mathrm s)=2088\,\mathrm m$

or just 2100 m if taking significant digits into account.