# Graphs depicting the relationship between velocity and time.

Visit our "Knowledge Hub" to explore various topics such as GCSEs and GCSE Physics. In this section, we will discuss velocity-time graphs. Velocity-time graphs provide information about velocity in relation to time, which can be used to calculate important variables such as acceleration and distance traveled.

Velocity-time graphs share similarities with distance-time graphs discussed previously. However, in a velocity-time graph, time is plotted on the x-axis while velocity is plotted on the y-axis.

Similar to a displacement-time graph, a velocity-time graph may have a negative gradient if there is a decrease in velocity.

Let's analyze the graph above. Initially, the velocity increases for the first 2 seconds and then remains constant for the next 3 seconds. Subsequently, the line starts to decline with a negative gradient. It's important to note that this doesn't imply that the object is moving backwards. Rather, it indicates a decrease in velocity while still moving in the same direction. To better understand, imagine getting into a car and accelerating to a consistent speed of 40 meters per second for 3 seconds, followed by applying the brakes and gradually slowing down until coming to a complete stop after 7 seconds.

Now, let's discuss the role of gradients on velocity-time graphs. The gradient on a velocity-time graph provides information about the acceleration of the object. A flat line on the graph indicates 0 acceleration, signifying a constant speed. On the other hand, a positive gradient represents acceleration, as velocity increases. Conversely, a negative gradient signifies deceleration, as velocity decreases.

To calculate the numerical value of acceleration using the gradient of the graph, divide the y-axis value by the x-axis value.

As an example, let's utilize the graph below to find the acceleration at 2 seconds.

The speed at 6 seconds.

1. At 2 seconds, the incline of the line indicates that the velocity increases by 5 meters per second for every passing second. Therefore, the acceleration must be 5 ms^(-2).

2. At 6 seconds, we experience deceleration at a rate of 13.33 ms^(-2), indicating an acceleration of -13.33 ms^(-2).

**Determining the covered distance **

Velocity-time graphs are also useful in determining the distance covered. To do so, we calculate the area beneath the graph's line. This would result in a simple shape that can be examined, and the area discovered should be maintained in the provided units. An example of this is displayed on the preceding page:

The area beneath the graph corresponds to a rectangle and two triangles, resulting in an area of 200. Thus, this graph represents a covered distance of 200 meters.

Determining the distance from a velocity-time graph is truly as effortless as calculating the area beneath the line, based on the numerical values found on the axes. Consequently, this can be segmented, allowing us to determine the distance covered within a specific timeframe, such as from the beginning up to the fourth second, or from the third to the sixth second. All that is required is to find the area beneath the line between these two points on the axis.

**Example**

Discover the following details from the provided graph:

**Region Color**

**Shape**

**Calculation**

**Area**

Purple

Triangle

½ (base)(height)

22.5

Yellow

Rectangle

(height)(width)

15

Red

Triangle

½ (base)(height)

12.5

Indigo

Geometric Shape with Three Sides

½ (measure of the base)(measure of the height)

60

**Total sum**

**110**

2. To determine the distance covered between the third and sixth second, we calculate the region beneath the graph solely within that time interval. This task is comparatively straightforward, as the region can be broken down into manageable portions and subsequently totaled.

Consequently, the distance traveled between the third and sixth second amounts to **80.5 meters. **

**A Digest of Velocity-Time Diagrams**

**Methods to ascertain…**

**Calculation**

Velocity

Obtain the corresponding value on the axis for any given moment

Acceleration

Compute the inclination of the line at a specific point (if it exhibits negativity, it indicates deceleration, sometimes referred to as retardation)

Distance covered

Determine the area enclosed beneath the line

### Explore another one of our articles

If you find yourself in the position of wanting to hang pictures or a new TV and you desire to add some wall decor to create a more unified and finished look in your room, it is important to consider the preparations required before taking up that hammer.In order to securely hang any heavy items such as

Last updated: 07:06 EDT, 18 May 2021Critics of the television program How to Save a Grand in 24 Hours have strongly criticized a mother who spent £300 per month on beauty products but claimed she couldn't afford to remedy the black mold that was growing in her son's bedroom.Anna Wallace, hailing from

Learn how to stream the latest drama, 'No Return,' starring Sheridan Smith. Looking to watch the captivating holiday drama, No Return, online? Discover where you can find the thrilling series.Strongly following the journey of Kathy (Sheridan Smith) and Martin Powell (Michael Jibson), a married couple

If you're interested in scheduling a doctor's appointment using the myGP app, you'll need to follow these steps on your smartphone:1. Input your mobile number and date of birth. It's important to note that this must be the mobile number you provided when registering at your GP surgery.2. Conduct a