Final Distance Calculator

Formula

The formula to calculate the final distance (d_f) is:

\[ d_f = d_i + (v_i \cdot t) + (0.5 \cdot a \cdot t^2) \]

Where:

\( d_f \) is the final distance
\( d_i \) is the initial distance
\( v_i \) is the initial velocity
\( t \) is the time
\( a \) is the acceleration

Definition

Final Distance: The total distance covered by an object after a certain period of time, given its initial distance, initial velocity, time, and acceleration. It is a crucial concept in physics and engineering, often used to determine the position of an object in motion under uniform acceleration.

Example

Let's say the initial distance (d_i) is 0 meters, the initial velocity (v_i) is 10 meters per second, the time (t) is 5 seconds, and the acceleration (a) is 2 meters per second squared. Using the formula:

\[ d_f = 0 + (10 \cdot 5) + (0.5 \cdot 2 \cdot 5^2) \]

We get:

\[ d_f = 0 + 50 + 25 = 75 \, \text{m} \]

So, the final distance is 75 meters.