A speeding motorist traveling 125 km/h passes a stationary police officer. The officer immediately begins pursuit at a constant acceleration of 11.2 km/h/s (note the mixed units).
(a) How much time will it take for the police officer to reach the speeder, assuming that the speeder maintains a constant speed? in seconds
(b) How fast will the police officer be traveling at this time? in km/h
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Homework Help: physics
Posted by Whitney on Wednesday, November 3, 2010 at 10:13pm.
A speeding motorist traveling 125 km/h passes a stationary police officer. The officer immediately begins pursuit at a constant acceleration of 11.2 km/h/s (note the mixed units).
(a) How much time will it take for the police officer to reach the speeder, assuming that the speeder maintains a constant speed? in seconds
(b) How fast will the police offic
To solve this problem, we need to use the equation of motion:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
(a) To find the time it will take for the police officer to reach the speeder, we need to consider that the initial velocity of the officer is 0 km/h (since they were stationary). The acceleration is given as 11.2 km/h/s. The speeder's velocity is constant at 125 km/h.
Using the equation:
v = u + at
We can rearrange the equation to solve for time:
t = (v - u) / a
Substituting the known values:
t = (125 - 0) / 11.2
t = 11.16 seconds
Therefore, it will take approximately 11.16 seconds for the police officer to reach the speeder.
(b) To find the speed of the police officer at this time, we can use the same equation:
v = u + at
However, this time we know the initial velocity of the officer is 0 km/h, the acceleration is 11.2 km/h/s, and the time is 11.16 seconds.
Substituting the values:
v = 0 + 11.2 * 11.16
v ≈ 125.152 km/h
Therefore, the police officer will be traveling at approximately 125.152 km/h at this time.