An object falls freely near Earth's surface. Which graph best represents the relationship between the object's kinetic energy and time elapsed during its fall?

Question

illustrate what the graph would look like

Answer 1

When an object falls freely near Earth's surface, its kinetic energy (KE) increases as its velocity increases due to gravity. The relationship between kinetic energy and time can be illustrated by considering a few key points:

1. Kinetic Energy Formula: The kinetic energy of an object is given by the formula: $$KE=\frac{1}{2}m{v}^2$$ where $m$ is the mass of the object and $v$ is its velocity.

2. Velocity Increases Over Time: In free fall, the velocity increases linearly with time due to the constant acceleration of gravity (approximately $9.81,{\text{m/s}}^2$) until the object hits the ground (or some other stopping factor).

3. Relationship Between KE and Time: Since the velocity increases linearly with time, the kinetic energy (which is proportional to the square of the velocity) will increase quadratically with time (since $v=g\cdot t$, where $g$ is the acceleration due to gravity). Therefore, KE will rise in a parabolic manner over time.

Graph Description

On a graph where the x-axis represents time elapsed (t) and the y-axis represents kinetic energy (KE):

• The graph will start at the origin (0,0), because at $t=0$, KE is zero (the object hasn't started falling).
• As time progresses, the curve of the graph will rise steeply and be a parabolic curve, showing that kinetic energy increases quadratically with time.
• The shape of the curve will look like the right side of a parabola opening upwards.

In summary, the graph of kinetic energy versus time during free fall will be a parabolic curve starting from the origin and rising steeply as time goes on.