Final answer:
a. The acceleration of the boat is 0.25 m/s^2. b. The boat will move a distance of 9 m in 12 s. c. The speed of the boat at the end of the 12-second interval is 3 m/s.
Step-by-step explanation:
a. To find the acceleration of the boat, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force is the forward push by the motor minus the resistive force due to the water. So the net force is 2.10 × 10^3 N - 1.80 × 10^3 N = 3.0 × 10^2 N. The mass of the boat is given as 1,200 kg. Using the formula F = ma, we can rearrange it to solve for acceleration: a = F/m = (3.0 × 10^2 N)/(1,200 kg) = 0.25 m/s^2.
b. To find how far the boat will move in 12 s, we can use the kinematic equation: d = v0t + 0.5at^2. Since the boat starts from rest, the initial velocity v0 is 0. The acceleration a is 0.25 m/s^2 and the time t is 12 s. Plugging these values into the equation, we get d = 0 + 0.5(0.25 m/s^2)(12 s)^2 = 0 + 0.5(0.25 m/s^2)(144 s^2) = 9 m.
c. To find the speed of the boat at the end of the 12-second interval, we can use the equation v = v0 + at. Since the boat starts from rest, the initial velocity v0 is 0. The acceleration a is 0.25 m/s^2 and the time t is 12 s. Plugging these values into the equation, we get v = 0 + (0.25 m/s^2)(12 s) = 3 m/s.