let us assume that it takes t seconds for the police car to catch Alex.
Distance traveled by Alex in t seconds, S1 = V* t = 40*t.
Distance traveled by the police car in t seconds, S2 = 0.5* (a * t2) [ as the police car starts for the rest, initial speed, u =0]
S2 = 0.5 * (4.0*t2) [ as the acceleration of the police car = 4 m/s2]
= 2t2
If the Police car catches Alex, then S1 = S2
40*t = 2t2
solution: t = 0 s, 20 s.
acceptable solution: t = 20 s [ as at t=0, Alex just crosses the Police car, it is not an acceptable solution]
The police car takes 20 sec to catch Alex. (ans)
Alex have to pull over a distance of S1= (40* 20) m = 800 m down the road. (ans)
or Test 100 pts. s: Horizontal motion: Speeder probe: Alex was driving on a nice Sunday...