Final answer:
The time it takes for a car to accelerate from 0 to 28.0 m/s with a 60.0-kg passenger experiencing a horizontal force of 400 N is approximately 4.2 seconds. This is calculated using Newton's second law to find the acceleration and then applying the equation of motion that relates final velocity, initial velocity, acceleration, and time.
Step-by-step explanation:
To determine the time it takes for a car to reach a velocity of 28.0 m/s when a 60.0-kg passenger experiences a horizontal force of 400 N, we must first find the acceleration. The acceleration can be calculated using Newton's second law, where the force (F) equals the mass (m) multiplied by the acceleration (a), F = ma. Given the mass of the passenger and the force experienced, we can solve for the acceleration:
a = F / m = 400 N / 60.0 kg = 6.67 m/s²
Now we can use the equation of motion that relates final velocity (v), initial velocity (v₀), acceleration (a), and time (t):
v = v₀ + at
Solving for time (t), knowing that the initial velocity (v₀) is 0 m/s since the car starts from rest, we get:
t = (v - v₀) / a = (28.0 m/s - 0 m/s) / 6.67 m/s² = 4.2 s
Therefore, it takes approximately 4.2 seconds for the car to reach 28.0 m/s.