Displacement Calculator

How to Calculate Displacement

Displacement is a fundamental concept in physics that describes the change in position of an object. Understanding how to calculate displacement is crucial for analyzing motion and solving various physics problems.

What is the Formula for Displacement?

The formula for displacement in uniform motion is:

\[ s = \frac{1}{2}(v_0 + v_t)t \]

Where:

• \(s\) is the displacement (in meters, m)
• \(v_0\) is the initial velocity (in meters per second, m/s)
• \(v_t\) is the final velocity (in meters per second, m/s)
• \(t\) is the time interval (in seconds, s)

What are the calculation steps?

1. Identify the initial velocity (\(v_0\)) and final velocity (\(v_t\)) of the object.
2. Determine the time interval (\(t\)) over which the motion occurs.
3. Ensure all quantities are in SI units (m/s for velocity and s for time).
4. Apply the formula: \(s = \frac{1}{2}(v_0 + v_t)t\)
5. Perform the calculation to find the displacement (\(s\)).

Example of Displacement Calculation

Let's calculate the displacement of a car that starts with an initial velocity of 10 m/s and reaches a final velocity of 20 m/s over a time interval of 5 seconds:

Given:

• Initial velocity (\(v_0\)) = 10 m/s
• Final velocity (\(v_t\)) = 20 m/s
• Time interval (\(t\)) = 5 s

Step 1: Apply the displacement formula

\(s = \frac{1}{2}(v_0 + v_t)t\)

\(s = \frac{1}{2}(10 + 20) \times 5\)

Step 2: Perform the calculation

\(s = \frac{1}{2} \times 30 \times 5\)

\(s = 15 \times 5 = 75\) meters

Therefore, the displacement of the car over the 5-second interval is 75 meters.

Diagram of Displacement

The following diagram illustrates the concept of displacement:

This diagram shows an object moving from an initial position (blue dot) to a final position (red dot). The green dashed line represents the displacement, which is the straight-line distance between the initial and final positions, regardless of the actual path taken by the object.