Question

Which graph correctly shows the relationship between kinetic energy and velocity of an object in motion? Illustrate the graph

Answer 1

The relationship between kinetic energy (KE) and velocity (v) of an object in motion is given by the formula:

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

where:
- \( KE \) is the kinetic energy,
- \( m \) is the mass of the object (a constant),
- \( v \) is the velocity.

From this equation, we can see that kinetic energy is proportional to the square of the velocity. Therefore, if you plot kinetic energy on the y-axis and velocity on the x-axis, the graph will be a parabola that opens upwards, indicating that as the velocity increases, the kinetic energy increases quadratically.

### Illustration of the Graph:
1. **X-axis**: Velocity (v)
2. **Y-axis**: Kinetic Energy (KE)
3. **Shape**: A parabolic curve that starts at the origin (0,0) and rises steeply as velocity increases.

If you were to visualize the graph, it would look something like this:

```
|
KE | *
| *
| *
| *
| *
| *
|*
+----------------
v
```

This graph illustrates that at low velocities, kinetic energy increases slowly, but at higher velocities, it increases much more rapidly due to the squaring effect.