Posted by bill on .
An unmarked police car traveling a constant 95km/h is passed by a speeder traveling 14km/h .Precisely 2.50s after the speeder passes, the police officer steps on the accelerator; if the police car's acceleration is 2.30m/s^2 , how much time passes before the police car overtakes the speeder after the speeder passes (assumed moving at constant speed)?

physics  college 
Elena,
The time of police car motion is t,
the time of the speeder motion is (t+2.5).
The distance covered by
 the police car is v(p) •t+at^2/2,
 by speeder is v(s)•(t+2.5).
v(p) •t + at^2/2 = v(s)•(t+2.5).
v(p) = 95 km/h = 26.4 m/s
v(s) = 140 km/h = 38.9 m/s
v(p) •t + at^2/2 = v(s)• t + v(s)• 2.5,
at^2/2 + [v(p) – v(s)] •t 2.5•v(s) = 0,
t^2 –(2/a)•[v(s) – v(p)] •t – 2.5•2/a = 0,
t^2 – 10.9t  84.6 = 0,
t = 5.24 s.
The total time is 5.24+2.5 = 7.74 s. 
physics  college 
bill,
i think their is a mistake, the answer is incorrect

physics  college 
Elena,
The solution is right. The mistake may be in calculations. Calculate it carefully.