A car accelerates from 10.0 m/s to 30 m/s at a rate of 3.5 m/s2. How far does it travel while accelerating?
s = [(v(fin) ² -v(init)²]/2•a
To find the distance traveled while accelerating, we can use the formula:
distance = (final velocity^2 - initial velocity^2) / (2 * acceleration)
Given:
- Initial velocity (u) = 10.0 m/s
- Final velocity (v) = 30 m/s
- Acceleration (a) = 3.5 m/s^2
Substituting these values into the formula, we get:
distance = (30^2 - 10.0^2) / (2 * 3.5)
Calculating this equation:
distance = (900 - 100) / 7
distance = 800 / 7
distance ≈ 114.29 meters
Therefore, the car travels approximately 114.29 meters while accelerating from 10.0 m/s to 30 m/s with an acceleration of 3.5 m/s^2.