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\,(\mathrm m)/(\mathrm s)=14.6\,(\mathrm m)/(\mathrm s)+\left(-1.2\,(\mathrm m)/(\mathrm s^2)\right)t\implies t=3.2\,\mathrm s`

Next, recall that

`\Delta x=x_f-x_0=\frac{v_f+v_0}2t`

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

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