Final answer:
The magnitude of the car's acceleration is -79 m/s².
Step-by-step explanation:
To find the magnitude of the car's acceleration, we can use the formula:
acceleration = (final velocity - initial velocity) / time
Given that the car reduces its velocity from 50 m/s to 13.8 m/s over a distance of 15 m, we can calculate the time it took using the formula for distance: distance = (initial velocity + final velocity) / 2 * time
Solving for time, we get time = distance / ((initial velocity + final velocity) / 2)
Substituting the values into the equation, we get time = 15 m / ((50 m/s + 13.8 m/s) / 2)
Calculating the time, we get time = 0.238 s
Finally, substituting the values into the acceleration equation, we get:
acceleration = (13.8 m/s - 50 m/s) / 0.238 s
Calculating the acceleration, we get acceleration = -79 m/s²