a speeding car is driving at 120 km/h when it passes a police cruiser that is driving at 100 km/h. One second later, the police cruiser accelerates uniformly at 15 km/h until it reaches a speed of 135 km/h. how long does it take the police cruiser to catch the car
You acceleration has the wrong units. Did you mean 15 kph/s or kph/hr?
Either way the car is only about 5.55 m ahead when the police car starts speeding up
xcar = vcar t + 5.55
xpol = vpol t + 1/2 a t^2
set equal to each other and solve
To find out how long it takes for the police cruiser to catch the car, we can analyze the situation using relative velocity.
Step 1: Determine the initial separation between the car and the police cruiser.
Since the car had already been driving at 120 km/h for a second, it would have covered a distance of (120 km/h) * (1/3600 hr/s) = 0.0333 km. Therefore, the initial separation between the car and the police cruiser is 0.0333 km.
Step 2: Determine the relative velocity of the police cruiser with respect to the car.
The relative velocity is the difference in velocities between the police cruiser and the car.
When the car is driving at 120 km/h and the police cruiser is driving at 100 km/h, the relative velocity is (120 km/h - 100 km/h) = 20 km/h.
When the police cruiser accelerates uniformly and reaches a speed of 135 km/h, the relative velocity becomes (135 km/h - 120 km/h) = 15 km/h.
Step 3: Calculate the time it takes for the police cruiser to catch the car.
Since time = distance / speed, we can use this formula to find the time.
The distance the police cruiser needs to cover to catch the car is the initial separation (0.0333 km). The speed at which it covers this distance is the relative velocity (15 km/h).
Therefore, the time it takes for the police cruiser to catch the car is:
Time = distance / speed = 0.0333 km / 15 km/h = (0.0333 km) / (15 km/h) = 0.0022 hours or 2.2 seconds.
So, it takes the police cruiser approximately 2.2 seconds to catch the car.