Plot a graph of distance versus time for an object falling freely under Gravity

To plot a graph of distance versus time for an object falling freely under the influence of gravity, we first need to understand the relationship between distance, time, and acceleration due to gravity. When an object is in free fall, it accelerates downwards at a constant rate, which is approximately 9.81 m/s² on Earth. This means that the distance it falls increases with the square of the time elapsed. Let's break this down step by step.

The Basics of Free Fall

When an object falls freely, it starts from rest (assuming it is dropped and not thrown). The key equations that govern its motion are derived from the laws of physics, specifically kinematics. The distance \( s \) fallen after time \( t \) can be expressed with the formula:

s = ut + (1/2)gt²

In this equation:

• s = distance fallen (in meters)
• u = initial velocity (in meters per second, which is 0 if dropped)
• g = acceleration due to gravity (approximately 9.81 m/s²)
• t = time (in seconds)

Setting Up the Graph

Since the object starts from rest, the initial velocity \( u \) is 0. This simplifies our equation to:

s = (1/2)gt²

Now, let's consider how we can plot this. We will calculate the distance fallen at various time intervals and then plot these points on a graph.

Calculating Distance at Different Time Intervals

Let’s calculate the distance fallen at 0, 1, 2, 3, 4, and 5 seconds:

• At \( t = 0 \): \( s = (1/2) \cdot 9.81 \cdot (0)² = 0 \) m
• At \( t = 1 \): \( s = (1/2) \cdot 9.81 \cdot (1)² = 4.905 \) m
• At \( t = 2 \): \( s = (1/2) \cdot 9.81 \cdot (2)² = 19.62 \) m
• At \( t = 3 \): \( s = (1/2) \cdot 9.81 \cdot (3)² = 44.145 \) m
• At \( t = 4 \): \( s = (1/2) \cdot 9.81 \cdot (4)² = 78.48 \) m
• At \( t = 5 \): \( s = (1/2) \cdot 9.81 \cdot (5)² = 122.625 \) m

Plotting the Graph

Now that we have our distance values, we can plot them on a graph where the x-axis represents time (in seconds) and the y-axis represents distance (in meters). The points we calculated will look like this:

• (0, 0)
• (1, 4.905)
• (2, 19.62)
• (3, 44.145)
• (4, 78.48)
• (5, 122.625)

When you plot these points, you will notice that the graph is a parabola opening upwards. This curvature indicates that the distance increases more rapidly as time goes on, which is characteristic of uniformly accelerated motion.

Interpreting the Graph

The shape of the graph tells us a lot about the motion of the object. Initially, the distance increases slowly, but as time progresses, the distance increases more dramatically. This reflects the fact that the object is accelerating due to gravity, meaning it falls faster and faster as time passes.

In summary, plotting the distance versus time for an object in free fall under gravity reveals a parabolic curve, illustrating the principles of kinematics and the effects of gravitational acceleration. This understanding is fundamental in physics and helps us analyze various motion scenarios.