Question

A car slows from 22 m/s to 3.0 m/s at a constant rate after 110 meters. How many seconds are required before the car is traveling 3.0 m/s?

Answer 1

Recall that average velocity is given by

$v_{\rm ave}=\dfrac{\Delta x}{\Delta t}$

Under constant acceleration, we also have

$v_{\rm ave}=\dfrac{v_i+v_f}2$

Then

$\dfrac{\Delta x}{\Delta t}=\dfrac{v_i+v_f}2$

$\implies\dfrac{110\,\mathrm m}{\Delta t}=\dfrac{22\frac{\rm m}{\rm s}+3.0\frac{\rm m}{\rm s}}2$

$\implies\boxed{\Delta t=8.8\,\mathrm s}$