# Velocity Time Graph Maker Calculator + Online Solver With Free Steps

The **Velocity Time Graph Maker Calculator** plots the velocity-time graph using the first equation of motion. **Motion** is defined as the change in the position of an object concerning time. The factors such as **velocity** and **acceleration** determine the motion of an object.

**Velocity** defines the direction in which the object is moving. It is the time **rate** of **change** in **distance**. It represents the object’s speed and direction and is a **vector** quantity. **Acceleration** is the **rate of change** in the **velocity** of an object. It is a **vector** quantity whose direction is the direction of the net force acting on the object.

The calculator takes these **parameters** of the first equation of motion as input and outputs the resulting velocity time graph. The first **equation of motion** is as follows:

**v = u + at**

Where** u** is the **initial velocity**, **a** is the **acceleration**,** v** is the **final velocity,** and **t** is the **time** taken. The equation of motion takes the body to be moving in a straight line.

The **velocities** are measured in meters per second, the **acceleration** in meters per second square, and time in seconds.

## What Is a Velocity Time Graph Maker Calculator?

**The Velocity Time Graph Maker Calculator is an online tool used to graph an object’s velocity time relationship by entering the initial velocity, acceleration, and elapsed time in the first equation of motion.**

The **initial velocity** **u** is the velocity with which the object starts moving. The object moves with uniform **acceleration** **a,** and after some **time t**, the velocity of the object changes to **v**. The object is moving in a straight line.

The **slope** of the line in the velocity-time graph gives the **object’s acceleration**. The **area** under the line in the **v-t graph** tells how much **distance** the object has covered.

## How To Use the Velocity Time Graph Maker Calculator

The user can use the** Velocity Time Graph Maker Calculator** by following the steps given below.

### Step 1

The user must first enter the acceleration in the calculator’s input window. It should be entered in the block labeled; “**Acceleration (m/s/s)**.”

The acceleration should be in the units of **meters per second squared**.

For the **default** example, the uniform acceleration of the object is taken as 4 m/s.s.

### Step 2

The user must now enter the object’s initial velocity in the calculator’s input window. It should be entered in the block titled; “**Initial Velocity (m/s)**.”

It should be in units of **meters per second**.

The initial velocity u is taken as 5 m/s in the **default** example.

### Step 3

The user must now enter the time taken by the object to change its velocity. It should be entered in the block labeled; “**time (t)**.”

The time taken should be in **seconds** by SI units.

For the** default** example, the time entered is 10 sec.

### Step 4

The user must now press the “**Plot**” button for the calculator to process the input values and plot the resulting velocity-time graph.

### Output

The calculator shows the output in the four windows given below.

#### Input Interpretation

The calculator interprets the input data and shows the parameters of the **first equation of motion** by placing them in the equation.

For the **default** example, the calculator shows the equation of motion as follows:

**v=4t+5 **where** t=0 **to** 10 sec**

#### Geometric Figure

The calculator also predicts the geometric figure of the resulting equation of motion. It also shows the option of “**Properties,**” which tells about the properties of the geometric figure.

The equation formed for the **default** example is the equation of a line; hence the calculator displays “**line**.”

#### Plot

The calculator shows the **velocity-time plot** in this window. In the graph, the **time** is the independent quantity; hence is on the **x-axis,** and the **velocity** is taken on the **y-axis**.

The **slope** of the line gives the acceleration of the moving object.

#### Arc Length of Curve

The calculator also provides the arc length of the curve. It also provides all the mathematical steps for the arc length of the curve calculation by clicking on “**Need a step-by-step solution to this problem?**”.

The arc length for the **default** example is 41.231.

## Solved Examples

The following examples are solved through the Velocity Time Graph Maker Calculator.

### Example 1

A body starts moving with an **initial velocity** of 6 m/s. After 7 seconds, the velocity of the moving body changes. It is now traveling with a uniform **acceleration** of 15 m/s.s.

Plot the **velocity time graph** for this case and find the curve’s arc length.

### Solution

The user must first enter the **parameters** for the equation of motion **v=u +at** as follows:

**Acceleration (a) = 15 m/s$^2$**

**Initial Velocity (u) = 6 m/s**

**Time (t) = 7 sec**

After entering the input data, the user must now press “**Plot**. The calculator shows the equation of motion as follows:

**v = 15t + 6** where** t = 0** to **7 sec**

The geometric figure formed is a “**line**.” **Figure 1** shows the velocity-time graph for this example.

The **arc length** of the curve is calculated as 105.23.

### Example 2

A body **accelerates** at 20 m/s.s with an **initial velocity** of 9 m/s in 13 seconds.

Plot the **velocity-time graph** using the equation v=u +at. Also, calculate the arc length of the curve.

### Solution

The values for **acceleration**, **initial velocity**, and** time** should be entered in the calculator’s input window as follows:

**Acceleration = 20 m/s.s**

**Initial Velocity = 9 m/s**

**Time = 13 sec**

After pressing “**Plot**,” the calculator shows the equation of motion in the **Input Interpretation** window as follows:

**v = 20t + 9** where **t = 0** to** 13 sec**

The calculator shows the **geometric figure** to be a “**line**” for the equation. The velocity-time graph of the particular equation is shown in **figure 2**.

The **arc length** of the curve is 260.32.

*All the images are created using GeoGebra.*