Ahighway patrolman traveling at the speed limit is passed by a car going 20 mph faster than the speed limit. after one minute, the patrolman speeds up to 115 mph. how long after speeding up until the patrolman catches up with the speeding car. the speed limit is 55 mph.
(b) same question, but this time the patrolman speeds up to a speed of v mph

It will take 40 seconds to catch the speeding car

Explanation:

Initial speed of the patrolman = 55 mph

after one minute speed of patrol man = 115 mph

now acceleration of patrolman is given by

now at this acceleration the distance covered by patrolman in "t" time is given as

now we know the speed of the speeding car is given as

now in the same time distance covered by it

now since the distance covered is same

true tan speed = ang vel x radius