The time for the police car to catch up with the speeding motorist is 7.6 seconds.
<h3>What time will the police car catch up with the speeding motorist?</h3>
The police car and the motorist will cover equal distances.
Let the distance covered be d.
Distance covered by the motorist = speed * time
time = t, speed = 30 m/s
d = 30t
Distance covered by the police car = acceleration * (time)
time = t - 2, acceleration = 5.0 m/s²
d = 5(t-2)²
d = 5(t² - 4t + 4)
d = 5t² - 20t + 20
Equating the two equations for distance
5t² - 20t + 20 = 30t
5t² - 50t + 20 = 0
Solving for t using the quadratic formula:
t = 9.6 second or 0.4 seconds
Since t > 2, t = 9.6 seconds
t - 2 = 9.6 - 2
t - 2 = 7.6 seconds
Therefore, the time for the police car to catch up with the speeding motorist is 7.6 seconds.
Learn more about distance and acceleration at: brainly.com/question/14344386
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