A car is speeding at 33.4 m/s. A police car starts in pursuit from rest when the car is 100 m past the cruiser. At what rate must the cruiser accelerate to catch the speeder before the state line, 1.2 km away from the speeding car?

Include all steps if possible please, so that I may fully understand.

d = r*t = 1200 m.

33.4t = 1200,
t = 1200 / 33.4 = 35.93 s. = Time to reach state line.

Dt = 100 + 1200 = 1300 m. = Dist. the
trooper must travel to reach state line.

Dt = 0.5a*t^2 = 1300 m.
0.5a*(35.93)^2 = 1300,
0.5a*1291 = 1300,
645.5a = 1300,
a = 1300 / 645.5 = 2.014 m/s^2.

To solve this problem, we can use the equations of motion to determine the rate at which the police cruiser must accelerate in order to catch up with the speeding car.

Step 1: Convert the speed of the speeding car to meters per second (m/s):
Given that the car is speeding at 33.4 m/s.

Step 2: Determine the time it takes for the police cruiser to catch up to the speeding car:
Let's call the time it takes for the police cruiser to catch up to the car as 't'. Since the police cruiser starts from rest, its initial velocity is 0 m/s. The distance covered by both the car and the police cruiser to meet can be considered as 'd'. Thus, the distance traveled by the police cruiser is 100 m less than the total distance between them, which is 1.2 km (or 1200 meters). So, the distance traveled by the police cruiser is:
d = 1200 m - 100 m = 1100 m

Using the equation of motion, s = ut + 0.5at^2, where s is the distance, u is the initial velocity, t is the time, and a is the acceleration, we can rearrange the equation to solve for time:
1100 = 0 + 0.5 * a * t^2
Simplifying the equation, we get:
550 = 0.5 * a * t^2

Step 3: Find the acceleration required by the police cruiser:
Since we are solving for acceleration, rearrange the equation to solve for 'a' by isolating it:
a = (550 * 2) / t^2

Now we need to find the value of 't'. To do that, we need to find the time it took for the car to travel the distance of 100 m beyond the police cruiser:
Using the equation s = ut + 0.5at^2, and given that s = 100 m and u = 33.4 m/s:
100 = 33.4 * t + 0.5 * 0 * t^2 (since the car is not accelerating)
100 = 33.4 * t
Simplifying, we find:
t = 100 / 33.4

Step 4: Substitute the value of 't' back into the equation for 'a':
a = (550 * 2) / (100 / 33.4)^2

Now we can solve this equation to find the acceleration 'a'.