A car speeds past a stationary police officer while traveling 135 km/h. the officer immediately begins pursuit at a constant acceleration of 11.8 km/h/s, just as the driver passes her.
a. how much time, in seconds, will it take for the police officer to catch up to the speeding car, assuming that the car maintains a constant speed?
b. how fast, in kilometers per hour, will the police officer be traveling at the time he catches up to the driver?

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Onyebuchinnajiid Onyebuchinnajiid · Answer 1

(a) The time it takes for the police officer to catch up to the speeding car is determined as 0.31 s.

(b) The speed of the police officer at the time he catches up to the driver is 136.8 km/h.

The time taken for the police to catch up with the driver is calculated as follows;

v = at

where;

t = v/a

t = 37.5/3.278

t = 11.4 seconds

(v1 - v2)t = ¹/₂at² --- (1)

(v1 - v2)t = v1²/2a --- (2)

From (1):

(v1 - 37.5)t = ¹/₂(3.278)t²

(v1 - 37.5)t = 1.639t²

v1 - 37.5 = 1.639t

v1 = 1.639t + 37.5 -----(3)

From (2):

(v1 - 37.5)t = v1²/(2 x 3.278)

(v1 - 37.5)t = 0.153 ----- (4)

solve 3 and 4;

(1.639t + 37.5 - 37.5)t = 0.153

1.639t² = 0.153

t² = 0.0933

t = 0.31 s

v1 = 1.639(0.31) + 37.5 = 38 m/s = 136.8 km/h

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