Velocity-Time Graph Analysis: Plotting Free Fall Motion of a Stone

Free Fall Motion with Linear Velocity

Choose the graph that best describes the following:

The velocity of a heavy stone (Y) after being dropped from a great height as a function of time (X).

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Choose the graph that best describes the following:

The velocity of a heavy stone (Y) after being dropped from a great height as a function of time (X).

2

Step-by-step solution

Since the velocity depends on the acceleration in a direct relationship, and since the acceleration is constant, the graph must have a straight slope.

Since the graph in answer D describes a constant function, this is the correct answer.

3

Final Answer

WeatherSpeed 000

Key Points to Remember

Essential concepts to master this topic
  • Physics Rule: Free fall has constant acceleration due to gravity
  • Graphing: Velocity = acceleration × time creates straight line from origin
  • Check: Linear graph passes through (0,0) with constant positive slope ✓

Common Mistakes

Avoid these frequent errors
  • Confusing velocity with position graphs
    Don't choose curved graphs for velocity in free fall = wrong physics concept! Position graphs are parabolic, but velocity graphs are linear. Always remember that constant acceleration produces linear velocity change over time.

Practice Quiz

Test your knowledge with interactive questions

In what domain does the function increase?

–20–20–20–10–10–10101010202020–10–10–10101010000

FAQ

Everything you need to know about this question

Why is the velocity graph a straight line?

+

In free fall, gravity provides constant acceleration (about 9.8 m/s²). Since velocity = acceleration × time, and acceleration is constant, the graph must be a straight line starting from zero.

What does the slope of the line represent?

+

The slope represents the acceleration due to gravity. A steeper slope means greater acceleration, while the slope stays constant throughout the fall.

Why does the line start at the origin (0,0)?

+

At time zero, the stone is just dropped (not thrown), so its initial velocity is zero. The line must pass through (0,0) since v = 0 when t = 0.

Would air resistance change this graph?

+

Yes! With air resistance, the acceleration decreases as velocity increases, making the graph curved rather than linear. But this problem assumes no air resistance.

How is this different from a position graph?

+

A position graph for free fall would be parabolic (curved) because position = ½gt². A velocity graph is linear because velocity = gt.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Functions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations