# 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:

• The total distance covered.
• The distance covered between 3 and 6 seconds.
• To determine the total distance covered, we must calculate the area beneath the line. This graph can be easily divided into segments that are either rectangular or triangular, enabling us to find the area of each segment and then add them together to obtain the complete area beneath the graph. This calculation results in a total distance of 110 m.
• 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

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