Suppose that a person unwisely drives 75 mih in a 55 mih zon

Suppose that a person unwisely drives 75 mi/h in a 55 mi/h zone and passes a police car going
55 mi/h in the same direction. If the police officers begin constant acceleration at the instant they are
passed and increase their speed to 80 mi/h in 4 s, how long does it take them to be even with the pursued
car?

Solution

The S be the distance covered by the unwise person before caught by police = the distance covered by police with with 55mi intial velocity and 4 sec of acceleration to 80 mil      = S = S1 +S2

time be the time taken for the police to caught = T and distance travelled S = 75 * T  

let S1 be the distance coverd by police during acceleration S1 = ut +at^2/2 ; u is intial velocity 55m ,

                                                              t accleration time = 4sec a = accleration = 80-55 / 4 = 6.25 m/s2

                           S1 = 270 m

and S2 be the distance covered by police car after accleration S2 = 80* (T-4)

                  S1+S2 = S

             270 + 80 (T- 4) = 75* T

               which gives T = 10 sec