A boat moves through the water with two forces acting on it. One is a 2.10 x 103 N forward push by the motor, and the other is a 1.80 x 103 N resistive force due to the water.
a. What is the acceleration of the 1200 kg boat?
b. If it starts from rest, how far will it move in l0.0 s?
c. What will its velocity be at the end of this time interval?
a. Well, well, well! Let's get to the bottom of this one. To find the acceleration of the boat, we need to apply Newton's second law. The total force acting on the boat is the forward push minus the resistive force, which gives us (2.10 x 10^3 N) - (1.80 x 10^3 N) = 0.30 x 10^3 N.
Now, we divide this total force by the mass of the boat (1200 kg) to get the acceleration. That gives us (0.30 x 10^3 N) / (1200 kg) = 0.25 m/s^2. Ta-da!
b. Oh, the suspense is killing me! If the boat starts from rest, we can use the formula s = ut + (1/2)at^2 to find the distance it moves in 10.0 seconds. Since the initial velocity is zero, the formula simplifies to s = (1/2)at^2. Plugging in the values, we get s = (1/2) * 0.25 m/s^2 * (10.0 s)^2 = 12.5 m. So, the boat will move a grand total of 12.5 meters.
c. The velocity at the end of the time interval can be found using the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time interval. Since the boat starts from rest, the initial velocity is zero. Plugging in the values, we get v = 0 + (0.25 m/s^2) * (10.0 s) = 2.5 m/s. The boat will be sailing at a speed of 2.5 meters per second at the end of the time interval. Bon voyage!
To find the acceleration of the boat, we can 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.
a. Applying this formula, the net force on the boat can be calculated as follows:
Net force = Forward push - Resistive force
= 2.10 x 10^3 N - 1.80 x 10^3 N
= 3.0 x 10^2 N
Using the formula F = m × a, where F is the net force, m is the mass of the boat, and a is the acceleration of the boat, we can rearrange the formula to solve for a:
a = F / m
= (3.0 x 10^2 N) / (1.2 x 10^3 kg)
= 0.25 m/s^2
Therefore, the acceleration of the boat is 0.25 m/s^2.
b. To find the distance traveled by the boat in 10.0 seconds, we can use the formula for distance traveled during constant acceleration:
d = v0 × t + 0.5 × a × t^2
Since the boat starts from rest, its initial velocity (v0) is 0 m/s. Plugging in the values, we get:
d = 0 × 10.0 s + 0.5 × (0.25 m/s^2) × (10.0 s)^2
= 0 + 0.5 × (0.25 m/s^2) × (100.0 s^2)
= 0 + 0.5 × 0.25 × 100.0 m
= 0 + 12.5 m
= 12.5 m
Therefore, the boat will move a distance of 12.5 meters in 10.0 seconds.
c. To find the final velocity of the boat at the end of the time interval, we can use the formula:
v = v0 + a × t
Since the boat starts from rest, its initial velocity (v0) is 0 m/s. Plugging in the values, we get:
v = 0 + (0.25 m/s^2) × (10.0 s)
= 0 + 2.5 m/s
= 2.5 m/s
Therefore, the velocity of the boat at the end of the time interval is 2.5 m/s.
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 its mass multiplied by its acceleration.
a. To calculate the acceleration, we need to subtract the resistive force due to water from the forward push by the motor:
Net Force = Forward Push - Resistive Force
Net Force = 2.10 x 10^3 N - 1.80 x 10^3 N
Net Force = 0.30 x 10^3 N
Now, we can use Newton's second law to find the acceleration:
Net Force = Mass x Acceleration
0.30 x 10^3 N = 1200 kg x Acceleration
Solving for acceleration:
Acceleration = (0.30 x 10^3 N) / (1200 kg)
Acceleration = 0.25 m/s^2
Therefore, the acceleration of the boat is 0.25 m/s^2.
b. To calculate the distance the boat will move in 10.0 seconds if it starts from rest, we can use the kinematic equation:
Distance = Initial Velocity x Time + (1/2) x Acceleration x Time^2
Since the boat starts from rest, the initial velocity is 0:
Distance = 0 x 10.0 s + (1/2) x 0.25 m/s^2 x (10.0 s)^2
Distance = 0 + (1/2) x 0.25 m/s^2 x 100.0 s^2
Distance = 0 + 12.5 m
Distance = 12.5 m
Therefore, the boat will move a distance of 12.5 meters in 10.0 seconds.
c. To calculate the velocity of the boat at the end of the time interval, we can use the kinematic equation:
Final Velocity = Initial Velocity + Acceleration x Time
Since the boat starts from rest, the initial velocity is 0:
Final Velocity = 0 + 0.25 m/s^2 x 10.0 s
Final Velocity = 2.5 m/s
Therefore, the velocity of the boat at the end of the time interval will be 2.5 m/s.