Question

g A motorist traveling at 30.0 m/s passes a stationary police car. The police car gives chase 2.0 s later, accelerating at 5.0 m/s2. How long after giving chase will the police car catch the motorist

Answer 1

The time for the police car to catch up with the speeding motorist is 7.6 seconds.

What time will the police car catch up with the speeding motorist?

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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