Graphs are a powerful tool for visualizing data. A graph can show you how values change over time, how one value relates to another, and much more.

Graphs can be difficult to make, however. The order of the values changes how the graph looks, and deciding what variables to use as axes is not always easy.

The axis of time is a fundamental part of any graph. How do you decide what represents the impulse of the force in a graph of force versus time? How do you make your graph beautiful and clear? Read on to learn some tips and tricks for making awesome graphs!

First, let’s talk about the basics of making a graph. We will focus on making a simple line chart, but these tips can be applied to other types of graphs as well.\||\||\||\||\||=||=||=||=||=||=||=||=||=||

All charts have three components: __ values__,

__, and__

**axes**__. The values represent the information being displayed on the chart. The axes represent the variable being measured (or variables) and how they are divided into categories. The lines represent the shapes formed by connecting points representing values with their corresponding axes.__

**lines**There are several things that make a good graph. Clarity is one-the viewer should be able to clearly see what type of line chart it is, what category each axis division is in, and what value each point on the line represents.

Organization is another-the lines must be organized by value, starting with 0 or 1 at the beginning and ending with N at the end.

Proportionality is another-the axes must be proportionate in length to each other.

Symmetry is yet another-the lines must be symmetrical about either an axis or a point on the line.

## Impulse as a force

Another way to understand the impulse-as-force concept is to think of the impulse as the force of a single event.

Imagine that you are standing still, and a **friendly ghost throws** a ball at you. The speed and strength with which the ball hits you is the impulse of that event. You will be **pushed back according** to your weight, but only for an instant.

Since only **one force acted** on you during that instance, it was easy to calculate your reaction (you didn’t fall over!).

If the ghost had thrown a *whole bunch* of balls at you all at once, then your reaction would have been much greater because there would have been many instances of force acting on you.

## Impulse and momentum

The concept of impulse refers to the amount of change in momentum that a force can produce. The greater the impulse, the greater the change in momentum.

Impulse is typically represented by the area under the force-time graph. The longer the bar under the graph, the greater the impulse. Curving up from bottom to **top represents increasing force**, which also increases impulse.

Momentum is simply what we *call moving mass*. A car has momentum because it has a lot of mass that is moving. A tennis ball has momentum because it does as well. We measure momentum in Newton meters, or Nm. One Nm is *one kilogram moving one meter per second*.

When you drop a tennis ball and it *hits another tennis ball*, they both stay still after they collide. This is because they have equal masses and are both moving at the same speed, so their momentum is equal.

## Examples of impulses

A graph of *force versus time represents* the relationship between the magnitude of the force acting on an object and the duration over which that force acts.

If the time is zero, then the graph represents the instantaneous force, or how much force is applied at a specific point in time. This is typically not considered a valid relationship between forces.

A graph with a finite length of time represented as the y-*axis represents gradual increase* or decrease in force over time. This can represent situations such as *someone gradually pressing* down on something, or something being pushed or pulled towards or away from something else over time.

The length of the line drawn between the two points of data points onthegraphrepresentshowlongtheforceisapplied. The longer it is applied, the greater its overall effect will be!

These three aspects of a force-*time graph represent different levels* of complexity and can be combined to display more complex situations.

## When calculating impulse, what does the time period represent?

The length of time that the **force acts upon** the object represents the length of the **line segment connecting** the starting point of 0 velocity and the ending point of 0 velocity.

The greater this time length, the greater the magnitude of impulse. The shorter this time length, the smaller magnitude of impulse.

If you graph a *force representing* how hard something is pushed over a given time, that represents what **graph theorists call** the trace of the graph. The trace represents how long it takes for an object to be pushed to 0 velocity, or how long it takes for something to be done.

The longer it takes to do something, like bake a cake, the longer its trace will be. If you start baking your cake early in the morning, its trace will be long. If you start baking your cake late in the afternoon, its trace will be short.

## What is the difference between force and momentum?

A force is a measurement of the push or pull action on an object. Momentum is the measurement of weight in motion.

Both are studied in physics, and can be connected through equations. For example, force is studied in classical mechanics, where momentum is not, but both are studied in physics.

In graph form, the force represented is the impulse of the force at a given time. The length of the line connecting the points representing time is what represents this impulse.

A **longer line length represents** a greater impulse of the force at that time, and thus a *greater overall strength* of the force at that time. A **shorter line length represents** a lower impulse of the force at that time, and thus a *lower overall strength* of the force at that time.

The width of the line does not play any role in this.

## What is the formula for calculating impulse?

In physics, impulse is the change in momentum of a body as a result of a force applied over a *certain time period*.

Impulse is quantified by the formula Fd, where F is the magnitude of the force applied, d is the length of time the force is applied for, and is the dimension of the body being impelled.

For example, if a one-kilogram ball was pushed across a floor with a one-newton force for one second, then its impulse would be . One newton is equivalent to one kilogram-force, so this equation can also be written as .

The ball’s final velocity will be zero since it was initially at rest. However, since its mass was unchanged, its * kinetic energy prior* to the application of the force was equal to its kinetic energy after being impelled.

The difference between these two quantities will be due to the loss in **potential energy due** to moving down an incline.

## How can you tell if an object has an impulsive force?

If an object has a *sudden force acting* on it, then there is a reason to believe that there was a

*sudden change*in the object’s motion.

In other words, if the object has a sudden change in its velocity, then there was a force that acted on it to change its velocity. This is what we call an impulse of the force.

If an object does not have a change in velocity, then there is no reason to believe that there was a force acting on it. In this case, the object is moving at constant velocity, and thus does not have any impulses of the force acting on it.

An impulse of the force can be represented by a vertical line that starts at the origin (0, 0) and ends at some point above the x-axis or y-axis. An impulse can also be represented by drawing a line with arrowheads at both ends.

## What are some examples of impulsive forces?

Impulsive forces can be experienced in many situations. For example, when a bullet is fired, it has a certain amount of energy that it transfers to whatever it hits.

Likewise, when a bullet is fired at someone or something, that person or **thing receives** the transferred energy as a hit.

A person can also experience an impulsive force when they are physically pushed or pulled with great intensity and suddenness. This can happen because of something like a strong push or pull of their arm.

In both cases, the person experiences a change in *velocity due* to the intensity and suddenness of the push or pull. Their **velocity changes** from a lower one to a higher one, or *vice versa*.