Question

A driver of a car traveling at 14.6 m/s applies the brakes, causing a uniform deceleration of 1.2 m/s2. How long does it take the car to accelerate to a final speed of 10.8 m/s? How far has the car moved during the braking period?

Answer 1

Recall that

$v_f=v_0+at$

It takes the car about 3.2 s to reduce its speed from 14.6 to 10.8 m/s, since

$10.8\,\dfrac{\mathrm m}{\mathrm s}=14.6\,\dfrac{\mathrm m}{\mathrm s}+\left(-1.2\,\dfrac{\mathrm m}{\mathrm s^2}\right)t\implies t=3.2\,\mathrm s$

Next, recall that

$\Delta x=x_f-x_0=\dfrac{v_f+v_0}2t$

Then the car undergoes a displacement of about 41 m, since

$\Delta x=\dfrac{10.8\,\frac{\mathrm m}{\mathrm s}+14.6\,\frac{\mathrm m}{\mathrm s}}2(3.2\,\mathrm s)\implies\Delta x=41\,\mathrm m$