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Taylor creates a table using the masses of four different objects that travel with the same velocity. She calculates the kinetic energy of the objects and adds it to her table.

Object | Mass (kg) | Kinetic energy (J)
A | 6 | 3
B | 8 | 4
C | 10 | 5
D | 12 | 6
How would a line graph look that shows the relationship between kinetic energy and mass?
A. It looks like a straight line slanting upwards.
B. It looks like a straight line slanting downwards.
C. It looks like a horizontal flat line.
D. It looks like a curve going down.

3 answers

To determine how the line graph would look that shows the relationship between kinetic energy and mass, we can analyze the data given. The kinetic energy is calculated using the formula:

\[ KE = \frac{1}{2} mv^2 \]

Since the velocity is constant for all objects, the kinetic energy should increase linearly with mass, as kinetic energy is directly proportional to mass in this scenario.

From the provided data:

  • For Mass = 6 kg, Kinetic Energy = 3 J
  • For Mass = 8 kg, Kinetic Energy = 4 J
  • For Mass = 10 kg, Kinetic Energy = 5 J
  • For Mass = 12 kg, Kinetic Energy = 6 J

If we plot these points on a graph with mass on the x-axis and kinetic energy on the y-axis, we see that as mass increases, the kinetic energy also increases.

Therefore, the correct answer describing how the line graph would look is:

A. It looks like a straight line slanting upwards.

are you positive this is correct

Let’s re-evaluate the situation based on the data you've provided:

  • Object A: Mass = 6 kg, Kinetic Energy = 3 J
  • Object B: Mass = 8 kg, Kinetic Energy = 4 J
  • Object C: Mass = 10 kg, Kinetic Energy = 5 J
  • Object D: Mass = 12 kg, Kinetic Energy = 6 J

Now, when we compare the mass and kinetic energy:

  • As you can see, as mass increases from 6 kg to 12 kg, the kinetic energy increases from 3 J to 6 J.
  • However, the relationship displayed in the data shows a specific proportionality: as the mass increases by increments of 2 kg (from 6 to 8 to 10 to 12), the kinetic energy increases by increments of 1 J (from 3 to 4 to 5 to 6).

This indicates a linear relationship, but the slope suggests a specific proportional increase rather than a direct proportional increase as per the kinetic energy equation.

Considering this data, when graphed, the relationship between mass and kinetic energy will indeed form a straight line slanting upwards, as aforementioned.

So to clarify, my initial assessment stands correct:

A. It looks like a straight line slanting upwards.

If you have any further details or context that might change this interpretation, please let me know!