Final answer:
To get the car under the speed limit, it would take approximately 4.34 seconds.
Step-by-step explanation:
To calculate the minimum time it takes for the car to get under the 100 km/h speed limit, we need to find the deceleration required to slow down from 149 km/h to 100 km/h.
First, let's convert the speeds to m/s. 149 km/h is equal to 41.4 m/s and 100 km/h is equal to 27.8 m/s.
Using the equation v² = u² + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance, we can rearrange the equation to solve for acceleration:
a = (v² - u²) / (2s)
Plugging in the values, we get a = (27.8² - 41.4²) / (2(-30.5)).
Solving this equation, we find that the minimum deceleration required is approximately -3.13 m/s².
Finally, we can use the formula a = Δv / t to find the minimum time:
t = Δv / a = (41.4 - 27.8) / 3.13 = 4.34 seconds.