We can break this problem into two parts: understanding the given information and solving for any unknowns.

Given:

• Initial distance from the dock: $d_0 = 12 \, \text{m}$
• Acceleration toward the dock: $a = 0.80 \, \text{m/s}^2$
• Initial velocity: $v_0 = 0 \, \text{m/s}$ (since the boat starts from rest)

We want to determine how long it takes for the boat to reach the dock.

We can use the second equation of motion for constant acceleration: $d = d_0 + v_0 t + \frac{1}{2} a t^2$ Since the boat starts from rest, $v_0 = 0$, and the boat needs to travel $d = 0$ (to reach the dock), the equation simplifies to: $0 = 12 + \frac{1}{2} \times 0.80 \times t^2$ Now let's solve for $t$.

$\frac{1}{2} \times 0.80 = 0.40$ $0 = 12 + 0.40 t^2$ $-12 = 0.40 t^2$ $t^2 = \frac{-12}{-0.40} = 30$ $t = \sqrt{30} \approx 5.48 \, \text{seconds}$

Answer:

The boat will take approximately 5.48 seconds to reach the dock.

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Do you want more details on this solution or have any other questions?

Here are 5 related questions to expand on this topic:

1. What would happen if the boat started with an initial velocity?
2. How would the time change if the acceleration were doubled?
3. What is the boat's velocity as it reaches the dock?
4. How much distance would the boat cover in the first 2 seconds?
5. Can we calculate the force required to accelerate the boat if its mass is given?

Tip: Always check units carefully when solving physics problems to ensure consistency and correctness.