Final answer:
The magnitude of the bicyclist's acceleration is 2.73 m/s², and the bicyclist traveled a total distance of 26.4 m during the time interval of 4.40 s.
Step-by-step explanation:
To determine the magnitude of the bicyclist's acceleration, we use the formula for acceleration a = Δv/Δt, where Δv is the change in velocity and Δt is the change in time. Since the bicyclist speeds up from rest (initial velocity vi = 0 m/s) to vf = 12.0 m/s in 4.40 s, the acceleration a is calculated as follows:
a = (vf - vi) / Δt = (12.0 m/s - 0 m/s) / 4.40 s = 2.73 m/s²
The correct answer for the acceleration is A. 2.73 m/s².
To find out how far the bicyclist traveled during the acceleration, we can use the equation of motion s = viΔt + 0.5a(Δt)². The distance s is calculated as follows:
s = (0 m/s)(4.40 s) + 0.5(2.73 m/s²)(4.40 s)² = 0 m + 0.5(2.73 m/s²)(19.36 s²) ≈ 26.4 m
The correct answer for the distance traveled is A. 26.4 m.