Answer: 2.45 s
Explanation;
To solve this problem, we can use one of the equations of motion:
final velocity² = initial velocity² + 2 × acceleration × distance
Since the car comes to a stop, the final velocity will be 0 m/s. We are given the acceleration (-5.00 m/s²) and the distance (15.0 m). We need to find the initial velocity first, and then we can find the time it took to stop.
0 = initial velocity² + 2 × (-5.00 m/s²) × 15.0 m
Solving for the initial velocity:
initial velocity² = 2 × 5.00 m/s² × 15.0 m = 150.0 m²/s²
initial velocity = √150.0 m²/s² ≈ 12.25 m/s
Now we can use another equation of motion to find the time it took to stop:
final velocity = initial velocity + acceleration × time
0 = 12.25 m/s + (-5.00 m/s²) × time
Solving for the time:
time = (12.25 m/s) / (5.00 m/s²) ≈ 2.45 s
So, it took approximately 2.45 seconds for the car to come to a stop.