Final answer:
The calculated final velocity of the car after undergoing acceleration over a distance of 345 m is approximately 58.2 m/s. However, this result does not match any of the answer choices provided in the question, indicating a possible error in the question or answer options.
Step-by-step explanation:
To determine how fast a car will be going after undergoing acceleration over a given distance, we can use the kinematic equation which relates initial velocity, final velocity, acceleration, and distance traveled:
v2 = u2 + 2as
Where:
v = final velocity
u = initial velocity
a = acceleration
s = distance
In this case, the car is initially traveling at 3 m/s (u) and undergoes an acceleration of 4.9 m/s2 (a) over a distance of 345 m (s). Plugging in these values, we get:
v2 = (3 m/s)2 + 2 * (4.9 m/s2) * (345 m)
v2 = 9 + 3381
v2 = 3390
v = √3390
v ≈ 58.2 m/s
However, none of the provided options (a) 22 m/s, (b) 5.4 m/s, (c) 15 m/s, or (d) 46.8 m/s matches the calculated speed. Thus, it appears there may be a mistake in the question or the options provided.