Different amounts of force are applied to the same boat over several trials, and the acceleration is measured. In a graph of acceleration versus net force, what does the slope of the graph represent?
the speed of the boat***
the mass of the boat
the inverse of the mass of the boat
the inverse of the speed of the boat
F = ma
where does speed come in?
The correct answer is: the acceleration of the boat.
The slope of the graph represents the relationship between the net force applied to the boat and the resulting acceleration. In this case, since the graph is of acceleration versus net force, the slope represents the acceleration. The speed and mass of the boat are not directly related to the slope of the graph.
To determine the meaning of the slope of a graph of acceleration versus net force, you need to understand the relationship between force and acceleration. According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
The formula for Newton's second law is expressed as F = m * a, where F represents the net force, m represents the mass of the object, and a represents the acceleration.
In the given scenario, different amounts of force are applied to the same boat, and the resulting accelerations are measured. If you were to plot a graph with acceleration (a) on the y-axis and net force (F) on the x-axis, the slope of the graph would represent the mass (m) of the boat.
Let's break it down further:
1. Rearranging the formula, we get: a = F / m
2. The slope of the graph represents the change in acceleration (delta a) divided by the change in net force (delta F) for different trials.
3. Mathematically, the slope (m_slope) of the graph is calculated as: m_slope = delta a / delta F
4. Comparing this with the formula a = F / m, we can deduce that the slope (m_slope) is equal to 1/m (inverse of the mass of the boat), as delta a and delta F are constant for the same boat.
5. Therefore, the correct answer is: the inverse of the mass of the boat.
In summary, the slope of the graph represents the inverse of the mass of the boat, not the speed of the boat.