Question

A car traveling at 7.0m/s accelerates uniformly at 2.5m/s square to reach a speed of 12m/s. How long does it take for this acceleration to occur?

Answer 1

When acceleration is constant, average and instantaneous acceleration are the same, so

$a=\dfrac{\Delta v}{\Delta t}=\dfrac{v-v_0}t\implies t=\dfrac{v-v_0}a$

Then

$t=\dfrac{12\,\frac{\mathrm m}{\mathrm s}-7.0\,\frac{\mathrm m}{\mathrm s}}{2.5\,\frac{\mathrm m}{\mathrm s^2}}$

$\implies t=2.0\,\mathrm s$