Calculating Final Velocity of a Speedboat

What is the velocity of the boat when it reaches the buoy?

Final answer: The speedboat moving at an initial speed of 30 m/s and slowing down uniformly at -3.5 m/s² over a distance of 100m will have a final velocity of about 5.7 m/s when it reaches the buoy.

Understanding the Solution:

Kinematics and Constant Acceleration: In this scenario, the speedboat is moving towards a no-wake buoy marker while decelerating with a constant acceleration. The fundamental concept employed to solve this problem is kinematics, which deals with the motion of objects without considering the forces causing the motion.

Equation of Motion: We utilize the kinematic equation v^2 = u^2 + 2as to determine the final velocity of the speedboat when it reaches the buoy. Here, v represents the final velocity, u is the initial velocity, a denotes acceleration, and s is the distance traveled.

Given Values: The initial velocity (u) of the speedboat is 30.0 m/s, the acceleration (a) is -3.5 m/s² (negative due to deceleration), and the distance traveled (s) is 100 meters.

Calculation: Substituting the values into the formula, we obtain v = √[(30.0 m/s)^2 + 2*(-3.5 m/s²)*100m]. Solving this expression yields approximately 5.7 m/s as the final velocity of the boat.

Therefore, the velocity of the boat when it reaches the buoy is around 5.7 m/s if it decelerates at a uniform rate of -3.5 m/s² from its initial speed of 30 m/s.