Final answer:
The acceleration of the sports car is 4.48 m/s² and this equates to approximately 0.458 g's when compared to the acceleration due to gravity. The correct answer is Option 1 a. 4.48 m/s², b. 0.458 g.
Step-by-step explanation:
To calculate the acceleration of the sports car, we use the formula a = Δv / Δt, where Δv is the change in velocity and Δt is the change in time. The sports car accelerates from rest (initial velocity, vi = 0) to a final velocity (vf = 27.8 m/s) over a period of time (t = 6.2 s).
Using the formula:
a = (vf - vi) / t = (27.8 m/s - 0) / 6.2 s = 4.48 m/s²
The acceleration due to gravity (g) is 9.8 m/s², so to find the number of g's, we divide the car's acceleration by the acceleration due to gravity:
Number of g's = a / g = 4.48 m/s² / 9.8 m/s² = 0.457 g (rounded to three decimal places)
Therefore, the correct answer is Option 1: a. 4.48 m/s², b. 0.458 g (rounded to three decimal places).