Final answer:
The final velocity of the BMW after accelerating at a rate of 0.77 m/s² for a distance of 0.400 km is approximately 29.53 m/s. This is calculated using the kinematic equation that incorporates initial velocity, acceleration, and distance.
Step-by-step explanation:
Final Velocity of a BMW Accelerating on a Highway
To determine the final velocity of the BMW after it has traveled 0.400 km with an acceleration of 0.77 m/s², we can use the kinematic equation that relates velocity, acceleration, and distance covered:
v² = u² + 2as
where:
- v is the final velocity,
- u is the initial velocity (16.0 m/s),
- a is the acceleration (0.77 m/s²),
- s is the distance covered (0.400 km converted to meters is 400 meters).
Let's plug the values into the equation:
v² = (16.0 m/s)² + 2 * (0.77 m/s²) * (400 m) = 256.0 m²/s² + 616.0 m²/s²
v² = 872.0 m²/s²
Taking the square root of both sides to find v:
v = √(872.0 m²/s²) ≈ 29.53 m/s
Therefore, the final velocity of the BMW is approximately 29.53 m/s.