Question

A police cruiser is traveling at 20.0 m/s when the officer spies a speeder. The cruiser accelerates at 3.0 m/s^2 for 5.0 seconds, at which time the speeder pulls over and starts thinking up excuses to try and get out of a ticket. The cruiser then slows to a stop at 5.0 m/s^2. How far does it go in the entire time?

Answer 1

For the first 5.0 seconds, the cruiser covers a distance of

$\left(20.0\dfrac{\rm m}{\rm s}\right)(5.0\,\mathrm s)+\dfrac12\left(3.0\dfrac{\rm m}{\mathrm s^2}\right)(5.0\,\mathrm s)^2=137.5\,\mathrm m$

At this point, the cruiser will have achieved a velocity of

$\left(20.0\dfrac{\rm m}{\rm s}\right)+\left(3.0\dfrac{\rm m}{\mathrm s^2}\right)(5.0\,\mathrm s)=35\dfrac{\rm m}{\rm s}$

The cruiser will take

$\left(35\dfrac{\rm m}{\rm s}\right)-\left(5.0\dfrac{\rm m}{\mathrm s^2}\right)t=0\implies t=7.0\,\mathrm s$

to come to a stop as it decelerates. It will have covered a total distance of

$(137.5\,\mathrm m)+\left(35\dfrac{\rm m}{\rm s}\right)(7.0\,\mathrm s)+\dfrac12\left(-5.0\dfrac{\rm m}{\mathrm s^2}\right)(7.0\,\mathrm s)^2=\boxed{260\,\mathrm m}$