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? (1 point)

Question

Responses

the inverse of the speed of the boat

the mass of the boat

the inverse of the mass of the boat

the speed of the boat

Answer 1

In a graph of acceleration versus net force, the slope of the graph represents the inverse of the mass of the boat. This is derived from Newton's second law of motion, \( F = ma \), which can be rearranged to \( a = \frac{F}{m} \). The slope (which is the change in acceleration divided by the change in force) indicates that for a given force, acceleration increases inversely with mass. Therefore, the correct response is:

the inverse of the mass of the boat.

Answer 2

Several motorboats with the same mass are used in an experiment. The forces of the different motors versus their accelerations are graphed. What is the y-intercept of this graph? (1 point)
Responses

the inverse of the mass

the mass

the velocity

zero

Answer 3

In a graph of force versus acceleration (where force is plotted on the x-axis and acceleration is on the y-axis) based on Newton's second law (\( F = ma \)), the relationship can be expressed as:

\[ a = \frac{F}{m} \]

If you rearrange this to the form of a linear equation (y = mx + b), you get:

\[ a = \frac{1}{m} F + 0 \]

In this equation, the slope is \(\frac{1}{m}\) (the inverse of the mass), and the y-intercept is 0. This means that when there is no force applied (F = 0), the acceleration (a) is also zero.

Therefore, the correct response for the y-intercept of the graph is:

zero.

Answer 4

Which situation describes an object that is accelerating?(1 point)
Responses

when the net force is zero

when the velocity increases

when equal forces act simultaneously

when the velocity is constant

Answer 5

An object is considered to be accelerating when there is a change in its velocity over time. This can happen in a few ways: if its speed increases or decreases, or if it changes direction.

From the options provided:

• When the net force is zero: This indicates that there is no acceleration (the object would either be at rest or moving at a constant velocity).
• When the velocity increases: This indicates acceleration, as the object's speed is changing.
• When equal forces act simultaneously: If equal forces act on the object in opposite directions, they would cancel each other out and result in no net force, meaning no acceleration.
• When the velocity is constant: This also indicates no acceleration, as the speed and direction are not changing.

Thus, the correct response that describes an object that is accelerating is:

when the velocity increases.

Answer 6

What happens to the acceleration when the net applied force acting on the box increases?

(1 point)
Responses

It decreases.

It becomes zero.

It increases.

It remains the same.

Answer 7

According to Newton's second law of motion, the acceleration \( a \) of an object is directly proportional to the net force \( F \) acting on it and inversely proportional to its mass \( m \). This relationship is expressed by the formula:

\[ a = \frac{F}{m} \]

From this equation, if the mass of the box remains constant and the net applied force increases, the acceleration will also increase.

Therefore, the correct response is:

It increases.