Final answer:
The distance that Ima traveled after applying the brakes with an initial velocity of 30.0 m/s and an acceleration of -8.0 m/s², is calculated using the kinematic formula. The calculated distance is 112.5 meters, which corresponds to answer A) 112.5 meters.
Step-by-step explanation:
The student is asking about the distance covered by a car with an initial velocity of 30.0 m/s as it comes to a stop when the brakes are applied. Given that the acceleration is -8.0 m/s², we can use the kinematic equation which relates initial velocity, acceleration, and distance covered:
v² = u² + 2as
Where:
- v is the final velocity (0 m/s since the car stops)
- u is the initial velocity (30.0 m/s)
- a is the acceleration (-8.0 m/s²)
- s is the distance traveled (which we want to find)
Rearranging the formula to solve for s, we have:
s = (v² - u²) / (2a)
Plugging in the values gives:
s = (0 - (30.0)²) / (2 × (-8.0))
s = (0 - 900) / (-16)
s = 900 / 16
s = 56.25 meters
Since Ima applies the brakes and skids to a stop, we must double the distance to account for the stopping distance during skidding:
Distance did Ima travel = 56.25 meters × 2
Distance = 112.5 meters
Therefore, the correct answer to the question is A) 112.5 meters.