Final answer:
The initial speed of the car is 15.0 m/s.
Step-by-step explanation:
To find the initial speed of the car, we can use the formula:
Final velocity = Initial velocity + (Acceleration * Time)
Given that the car slows down at a rate of -5.00 m/s² until it comes to a complete stop and travels a distance of 15.0 m, we can substitute the given values into the formula:
-5.00 m/s² * Time = -15.0 m
To find the time, we can rearrange the equation as follows:
Time = -15.0 m / -5.00 m/s² = 3.00 s
Substituting the value of time back into the formula:
Final velocity = Initial velocity + (-5.00 m/s² * 3.00 s)
Simplifying the equation:
0 m/s = Initial velocity - 15.0 m/s
Initial velocity = 15.0 m/s