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.

Distance Formula

Definition: The distance formula calculates the distance between two points in a plane.

Formula: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

\( d \): Distance
\( x_1, y_1 \): Coordinates of the first point
\( x_2, y_2 \): Coordinates of the second point

Example: \( d = \sqrt{(5 - 1)^2 + (7 - 3)^2} \)

\( d \): Distance
\( x_1, y_1 \): (1, 3)
\( x_2, y_2 \): (5, 7)

Following Distance Calculation

Definition: Following distance is the space between your vehicle and the vehicle ahead, measured in time.

Formula: \( t = \frac{d}{v} \)

\( t \): Time (seconds)
\( d \): Distance (meters)
\( v \): Speed (meters per second)

Example: \( t = \frac{50}{10} \)

\( t \): Time
\( d \): 50 meters
\( v \): 10 meters per second