Final answer:
The time taken by the police car to catch up to the car is 36 hours. The distance traveled by the police car when this happens is 2592 kilometers.
Step-by-step explanation:
In order to find the time taken by the police car to catch up to the car, we need to use the equation of motion for the police car. The equation is given by:
x = xo + vot + 1/2at^2
In this case, xo (initial position) and vo (initial velocity) are both 0 since the police car starts from rest. The acceleration, a, is given as 4 m/s^2. We can substitute these values into the equation and solve for t:
x = 0 + 0*t + 1/2*4*t^2
Simplifying the equation:
x = 2t^2
Now we can find the time taken by the police car to catch up to the car by substituting the distance traveled by the car (x) into the equation:
72*t = 2t^2
Simplifying the equation:
t = 36
Therefore, it will take the police car 36 hours to catch up to the car.
To find the distance traveled by the police car when it catches up to the car, we can substitute the time (t) into the equation for the police car:
x = 0 + 0*t + 1/2*4*t^2
Simplifying the equation:
x = 2t^2
Substituting the value of t:
x = 2*(36)^2
Simplifying the equation:
x = 2592
Therefore, the police car will have traveled a distance of 2592 km when it catches up to the car.