Understanding Free Fall: Calculating Speed at Different Times

In free fall under the influence of gravity, an object experiences acceleration. Near the surface of the Earth, this acceleration (often denoted as g) is approximately 9.81 m/s2. This guide will help you understand how to calculate the speed of an object in free fall at different times, using the principles of kinematics.

Introduction to Free Fall

In free fall, an object is subject only to the force of gravity, and it accelerates at a constant rate of 9.81 m/s2. This means that if you know the initial speed of the object, you can calculate its speed at any point in time using a simple formula.

Speed Calculation for Free Fall

Let's start by calculating the speed of an object initially moving downward at 30 m/s one second later and two seconds later.

Speed One Second Later

Given the initial speed v? 30 m/s, the acceleration due to gravity a 9.81 m/s2, and the time t 1 s:

The formula to use is:

v v? a·t

Substituting the given values into the formula:

v 30 m/s 9.81 m/s2·1 s 39.81 m/s

Speed Two Seconds Later

Now, let's calculate the speed after 2 seconds:

Given: v? 30 m/s, a 9.81 m/s2, and t 2 s:

v 30 m/s 9.81 m/s2·2 s 49.62 m/s

Summary of Speeds

Speed one second later: 39.81 m/s

Speed two seconds later: 49.62 m/s

Near Earth Gravity and Rounding Off

Near the surface of the Earth, the acceleration due to gravity is standardized as -9.80665 m/s2. This constant value is approximately 9.81 m/s2, depending on the level of accuracy required. If the initial speed is -25 m/s (downward), the velocity after acceleration would be:

v -25 m/s 9.81 m/s2 -15.19 m/s

Rounding to two significant figures, the velocity would be 50 m/s (downward).

Common Mistakes and Tips

Here are some common mistakes to avoid and a helpful formula to memorize:

Do not confuse the initial speed with the final speed. Ensure you understand the direction of the velocity (downward is negative, upward is positive). Use the kinematic formula: v u at.

For example, if you know the initial velocity u 30 m/s, the time t 1 second, and the acceleration a 10 m/s2, you can calculate the final velocity v using:

v 30 m/s 10 m/s2·1 s 40 m/s

This formula is also known as the SUVAT formula, where S is displacement, U is initial velocity, V is final velocity, A is acceleration, and T is time.

Conclusion

Mastering the calculation of speed in free fall is essential for understanding basic physics. By using the appropriate kinematic equations and formulas, you can accurately determine the velocity of an object at any given time during its free fall.

Keywords

Free fall Acceleration due to gravity Kinematic equations

Further Reading

For more information on free fall and kinematics, refer to resources like Guides on Free Fall Calculations and Resources on Kinematic Equations.