An unmarked police car traveling a constant 90 km/h is passed by a speeder. Precisely 2.00 s after the speeder passes, the police officer steps on the accelerator.

If the police car accelerates uniformly at 2.00 m/s^2 and overtakes the speeder after accelerating for 7.00 s, what was the speeder's speed in km/h?

I got 28.57 m/s (without converting to km/h yet). And I'm not sure if that's correct.

That can't be correct. The speeder must be traveling faster than the police car (90 km/h).

Sorry! I just noticed your answer had not been converted to km/h. You don't show how you got your answer, so it's impossible to tell where you might have made an error.

The answer I get, 29.45 m/2, is close to yours.

To solve this problem, we need to break it down into several steps:

Step 1: Convert the speed of the police car from km/h to m/s.
Given that the police car is traveling at a constant speed of 90 km/h, we need to convert it to m/s. We can multiply the speed in km/h by 1000/3600 to convert it to m/s.
90 km/h = (90 * 1000) / 3600 = 25 m/s.

Step 2: Calculate the distance traveled by the police car when it begins to accelerate.
Since the police car is traveling at a constant speed until the speeder passes it, the distance traveled by the police car is given by the formula: distance = speed * time. In this case, the time is 2.00 seconds, and the speed is 25 m/s. Therefore, the distance traveled by the police car is:
distance = 25 m/s * 2.00 s = 50 meters.

Step 3: Calculate the acceleration distance traveled by the police car.
The distance traveled during acceleration can be calculated using the formula: distance = initial velocity * time + 0.5 * acceleration * time^2. In this case, the initial velocity is 25 m/s, the time is 7.00 seconds, and the acceleration is 2.00 m/s^2. Plugging in these values, we get:
distance = 25 m/s * 7.00 s + 0.5 * 2.00 m/s^2 * (7.00 s)^2
distance = 175 m + 0.5 * 2.00 m/s^2 * 49.00 s^2
distance = 175 m + 49.00 m
distance = 224 meters.

Step 4: Calculate the speed of the speeder.
The speed of the speeder can be calculated by determining the average speed of the police car during the acceleration phase. Since the police car covered a total distance of 224 meters during this period, and the time it took was 7.00 seconds, we can calculate the average speed as follows:
average speed = distance / time
average speed = 224 m / 7.00 s
average speed = 32 m/s.

Step 5: Convert the speed of the speeder from m/s to km/h.
To find the speed of the speeder in km/h, we need to convert the average speed from m/s to km/h. We can do this by multiplying the average speed by 3600/1000:
speed in km/h = average speed * 3600/1000
speed in km/h = 32 m/s * 3600/1000
speed in km/h = 115.2 km/h.

Therefore, the speed of the speeder is approximately 115.2 km/h.