Final answer:
The distance traveled by a car accelerating from rest at 3.8 m/s^2 for 7.0 seconds is calculated using the formula d = (1/2)at^2, resulting in 93.1 meters. Option A is closest to this calculation, indicating a possible typo.
Step-by-step explanation:
To find the distance traveled by a car accelerating at a given rate until it reaches a certain velocity, you can use the formula for distance under constant acceleration:
d = ut + (1/2)at2
where d is the distance, u is the initial velocity, a is the acceleration, and t is the time. Given that the car accelerates from rest (initial velocity u = 0), the formula simplifies to:
d = (1/2)at2
Using the given values, acceleration a = 3.8 m/s2 and time t = 7.0 s, we can calculate the distance as follows:
d = (1/2) * 3.8 m/s2 * (7.0 s)2 = 0.5 * 3.8 * 49 = 93.1 m
The answer closest to our calculation is Option A) 107.8 m, which suggests either a rounding difference in the options provided or a typo in the question. However, the method to calculate the distance is demonstrated correctly here.