# How to calculate displacement from velocity time graph

In physics, displacement is a key concept that allows us to measure an object’s overall change in position. One way to determine such displacement is by analyzing a velocity-time graph. In this article, we will discuss the basics of a velocity-time graph and the step-by-step process of calculating displacement from it.

**Understanding Velocity-Time Graphs**

A velocity-time (v-t) graph represents an object’s velocity (the rate of change in the object’s position) plotted against time. On this graph, the x-axis represents time (t), and the y-axis represents velocity (v). The slope of the line at any given point illustrates the acceleration of an object at that point in time, while the area under the curve or lines represent displacement.

**Steps to Calculate Displacement from a Velocity-Time Graph**

**Step 1: Identify Key Data Points**

The first step is to identify key data points on the v-t graph. These points include the starting and ending times (t1 and t2) and their corresponding velocities (v1 and v2).

**Step 2: Determine Time Intervals**

Calculate the time intervals (Δt) by subtracting t1 from t2. This value represents the elapsed time during which the object was in motion.

**Step 3: Calculate Average Velocity**

To determine average velocity, add v1 and v2, then divide by 2:

Average velocity = (v1 + v2) / 2

**Step 4: Calculate Displacement**

Finally, apply the following formula to find the displacement:

Displacement = Average velocity × Δt

**Example Problem**

Let’s apply these steps to a sample problem:

Given a v-t graph with initial velocity (v1) = 5 m/s at t1 = 0 s, final velocity (v2) = 15 m/s at t2 = 4 s, calculate the displacement of the object.

Step 1: Identify key data points: v1 = 5 m/s, t1 = 0 s, v2 = 15 m/s, t2 = 4 s.

Step 2: Calculate Δt: Δt = t2 – t1 = 4 s – 0 s = 4 s.

Step 3: Calculate Average velocity: Average velocity = (v1 + v2) / 2 = (5 m/s + 15 m/s) / 2 =10 m/s.

Step 4: Calculate Displacement: Displacement = Average velocity × Δt = 10 m/s × 4 s = 40 meters.

**Conclusion**

Understanding how to calculate displacement from a velocity-time graph is an essential skill in physics. By following these steps, you’ll be able to determine the displacement of an object by simply analyzing its v-t graph. This will help you solve various motion-related problems and deepen your understanding of the concepts of physics.