Final answer:
The bicyclist traveled approximately 18.7 meters during the given time.
Step-by-step explanation:
To find the distance traveled by the bicyclist, we can use the equation:
distance = initial velocity × time + (1/2) × acceleration × time²
Given:
Initial velocity (u) = 0 m/s (starting from rest)Final velocity (v) = 11.0 m/sTime (t) = 3.40 s
Acceleration (a) = ? (to be found)
We can rearrange the equation to solve for acceleration:
distance = 0 × time + (1/2) × acceleration × time²
distance = (1/2) × acceleration × time²
Plugging in the given values, we get:
distance = (1/2) × acceleration × (3.40 s)²
Simplifying further:
distance = (1/2) × acceleration × 11.56 s²
Since we are looking for distance, we need to solve for acceleration:
acceleration = (2 × distance) / (time²)
Plugging in the given values, we get:
acceleration = (2 × distance) / (3.40 s)²
Now we can solve for acceleration:
acceleration = (2 × distance) / 11.56
Given that the final velocity is 11.0 m/s, we can use the equation:
final velocity = initial velocity + acceleration × time
Plugging in the given values, we get:
11.0 m/s = 0 m/s + acceleration × 3.40 s
Now we can solve for acceleration:
acceleration = 11.0 m/s / 3.40 s
Finally, we can substitute the value of acceleration back into the equation for distance:
distance = (2 × (11.0 m/s / 3.40 s)) / 11.56
Calculating this expression, we find that the distance traveled by the bicyclist during the given time is approximately 18.7 meters.