A boat initially at rest accelerates uniformly to $29.4 m / s$ over 7.60 s. What is the acceleration of the boat? $a=[?] m / s^2$
Answer (1)
Apply the formula for uniform acceleration: v f = v 0 + a \t .
Substitute the given values: 29.4 = 0 + a \t 7.60 .
Solve for a : a = 7.60 29.4 = 3.8684210526315788 m / s 2 .
Round the result to three significant figures: 3.87 m / s 2 .
Explanation
Problem Analysis We are given that a boat starts at rest and accelerates uniformly to a final velocity of 29.4 m / s over a time interval of 7.60 s . We need to find the acceleration of the boat.
Formula Introduction We can use the formula for uniform acceleration, which relates the final velocity ( v f ), initial velocity ( v 0 ), acceleration ( a ), and time ( t ): v f = v 0 + a \t
Substitution In this case, the initial velocity v 0 = 0 m / s , the final velocity v f = 29.4 m / s , and the time t = 7.60 s . Substituting these values into the formula, we get: 29.4 = 0 + a \t 7.60
Solving for Acceleration Now, we solve for the acceleration a :
a = 7.60 29.4 a = 3.8684210526315788 m / s 2 Rounding to three significant figures, we get: a ≈ 3.87 m / s 2
Final Answer Therefore, the acceleration of the boat is approximately 3.87 m / s 2 .
Examples
Understanding the acceleration of a boat is crucial in naval engineering and ship design. For example, when designing a tugboat, engineers need to calculate the required acceleration to ensure it can effectively tow larger vessels. This involves applying the principles of uniform acceleration to determine the necessary force and power to achieve the desired performance. Similarly, in competitive sailing, knowing the acceleration characteristics helps sailors optimize their strategies for quick starts and maneuvers, enhancing their overall performance in races.
