Final answer:
The answer involves using kinematic equations to determine the time taken for the bicycle to accelerate to its final velocity and then calculating the distance it traveled during this acceleration period.
Step-by-step explanation:
The correct answer is option B. To find the distance the bicycle traveled while accelerating, we can use the kinematic equation:
s = ut + \frac{1}{2}at^2
Where:
- u is the initial velocity (8 m/s)
- a is the acceleration (0.4 m/s²)
- t is the time it takes to reach the final velocity.
To find the time t, we use the formula:
v = u + at
Where:
- v is the final velocity (12 m/s)
Now, we can solve for t:
12 m/s = 8 m/s + (0.4 m/s²)(t)
(12 m/s - 8 m/s) / 0.4 m/s² = t
10 s = t
With the time known, we can now plug it back into the distance equation:
s = 8 m/s(10 s) + \frac{1}{2}(0.4 m/s²)(10 s)^2
s = 80 m + 20 m
s = 100 m
The distance traveled is double that which is required to reach the final velocity, which should alert the tutor to a potential mistake, and prompt revisiting the calculations.