Question

Olivia obtains the masses of four different objects. Each object travels with a velocity of 1 m/s. She calculates the kinetic energy of each object. She records the mass and the kinetic energy of each object in the table below.


Object Mass (kg) Kinetic energy (J)
A 2 1
B 4 2
C 6 3
D 8 4

If she makes a line graph showing the relationship between kinetic energy and mass at a constant velocity, how does the line look?

Group of answer choices

It looks like an S-curve.

It looks like a horizontal line.

It looks like a straight line slanting upwards.

It looks like a straight line slanting downwards.

Answer 1

To determine the relationship between kinetic energy and mass at a constant velocity, we can use the formula for kinetic energy (KE):

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

where \( m \) is the mass of the object and \( v \) is its velocity. In this case, the velocity is constant at 1 m/s, so the formula simplifies to:

\[
KE = \frac{1}{2}m(1)^2 = \frac{1}{2}m
\]

This shows that kinetic energy is directly proportional to mass. Therefore, if we plot mass on the x-axis and kinetic energy on the y-axis, we get a straight line that slants upwards, indicating that as mass increases, the kinetic energy also increases.

Given the data in the table:

- For Object A: \( 2\, \text{kg} \rightarrow 1\, \text{J} \)
- For Object B: \( 4\, \text{kg} \rightarrow 2\, \text{J} \)
- For Object C: \( 6\, \text{kg} \rightarrow 3\, \text{J} \)
- For Object D: \( 8\, \text{kg} \rightarrow 4\, \text{J} \)

The kinetic energies also follow a linear pattern where:
- Mass 2 kg corresponds to 1 J
- Mass 4 kg corresponds to 2 J
- Mass 6 kg corresponds to 3 J
- Mass 8 kg corresponds to 4 J

Thus, when graphed, it will produce a straight line slanting upwards.

**The answer is: It looks like a straight line slanting upwards.**