Question

or Test 100 pts. s: Horizontal motion: Speeder probe: Alex was driving on a nice Sunday afternoon enjoying the weatheoin not realizing he was doing a constant 40 m/s in a zone where he should have been doing 19 m/s. He drives past a police car hiding behind a tree who immediately takes off after him accelerating at a rate of 4.0 m/s2. How long until the police catches up to Alex. How far down the road wili Alex have to pull over? PIO astical notion

Answer 1

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)