Question

What are Velocity-Time Graph and Displacement-Time Graph?

Answer 1

A graph is defined as a pictorial representation of information which is a two-dimensional drawing explaining the relationship between dependent and independent variables.

Velocity-Time graph:

In the velocity-time graph, velocity is the dependent variable and is represented on the y-axis and time is the independent variable, represented on the x-axis. The slope of the graph will be:

$\frac{∆\mathrm{v}}{∆\mathrm{t}}$

Here,

“t” is the time.

“v” is the velocity.

The slope of the velocity-time graph is the definition of acceleration, therefore it can be said that the slope is equal to the acceleration.

1. The steep slope represents the rapid change in velocity.
2. The shallow slope represents the slow change in velocity.
3. If the slope is negative, then the acceleration will also be negative.
4. If the slope is positive, then the acceleration will also be positive.
5. The area under the velocity represents the displacement of the object.

Displacement-time graph

Displacement of an object is defined as how far the object is from its initial point. In the displacement time graph, displacement is the dependent variable and is represented on the y-axis while time is the independent variable and is represented on the x-axis and is also known as a position-time graph.

There are three different plots from the displacement time graph and they are given below:

1. The first graph explains that the object is stationary for a period of time such that the slope is zero which means that the velocity of the object is zero.
2. The second graph explains that the velocity of the object is constant and increases with time such that the slope of the graph remains constant and positive.
3. The third graph explains that the acceleration, velocity, and displacement are constant. The slope of the graph increases with time.

The slope for the displacement time graph will be:

$\frac{∆\mathrm{d}}{∆\mathrm{t}}$

Here,

“d” is the displacement.

“t” is the time.

The takeaway from the displacement time graph is as follows:

1. The slope is equal to velocity.
2. Constant velocity is explained by the straight line while the acceleration is explained by the curved lines.
3. A positive slope means the motion is in the positive direction.
4. A negative slope means the motion is in the negative direction.
5. Zero slope means that the object is at rest.