A car speeds past a stationary police officer while traveling 135 km/h. The officer immediately begins pursuit at a constant acceleration of 11.8 km/h/s, just as the driver passes her. A. How much time, in seconds, will it take for the police officer to catch up to the speeding car, assuming that the car maintains a constant speed?
B. How fast, in kilometers per hour, will the police officer be traveling at the time he catches up to the driver?

The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a vertical plane with constant angular velocity \omega. write down the lagrangian for a bead of mass m threaded on the rod, using r as your generalized coordinate, where r, \phi are the polar coordinates of the bead. (notice that \phi is not an independent variable since it is fixed by the rotation of the rod tobe \phi = \omega * t) solve lagrange's equation for r(t). what happens if the bead is initially at rest at the origin? if it is released from any point ro > 0, show that r(t) eventually grows exponentially. explain your results in terms of the centrifugal force m* \omega ^2 *r.