### What are the different types of mathematical relationships?

Physics A bigger diameter means a bigger circumference. In an inverse relationship, an increase in one quantity leads to a corresponding. to mass? Physics 2D Motion Relative Motion. 2 Answers. JINGYI Z. Apr 28, Answer: acceleration equals to the force applied divided by mass Thus, the LHS also doubles, meaning we get double the force: 2F=2m⋅a You can also see the inverse relation between m and a by solving F=ma for one or the other. M.1 Linear Motion; M.2 Vectors and Scalars; M.3 Newton's Laws; M.4 Momentum; M.5 Proportional; Inversely proportional; Proportionality; Constant of proportionality In physics, we often talk about proportionality. If we look at our previous two examples: \[\text{amount of chocolate} \propto \text{price.

Think about a long journey to see some family. The speed you travel at is related to the time the journey takes, but not in the same way as above.

## Inverse Proportion

As you increase your speed, the journey time decreases instead. In fact travelling twice as fast will cut the journey time in half. We call this type of relationship inverse proportionality.

If one quantity increases by a certain factor, the other quantity decreases by that same factor. We use the same symbol as for proportionality, but represent one quantity by its inverse, so: Proportion Equations All proportional relationships can be rewritten in the form of an equation with a constant of proportionality.

So our proportional relationship can be rewritten from: If we look at our previous two examples: We will use this fact in several parts of the course.

Other Proportional Relationships Proportional relationships can get more complicated than simply directly or inversely proportional. Very often quantities depend on the square root or cube of another quantity. One relationship we will see a number of times on the course is called inverse square proportionality.

For example we will later see that the force between two masses due to gravity is inversely proportional to the square of the distance between the masses, or: To put it simply, the equation that holds our two variables looks like the following: Here, y and x are our variables, and a, b, and c are constants.

If you didn't have this equation, and only had some data points for a graph, you'd be able to tell it's a quadratic relation if the graph's curve forms a parabola, which on a graph looks like a dip or a valley. Even if we have an equation like this where b and c both equal zero, it's still considered quadratic. If that happens, we get the simplest form of a quadratic relationship: This works because it turns out that it's the x squared component that's absolutely necessary for a relationship to be quadratic.

So, unlike b and c, a must never equal zero because that will remove the x squared from the formula since zero multiplied by anything is zero. One of the first places you'll encounter a quadratic relation in physics is with projectile motion.

This makes sense if you think about how a projectile travels through the air over time. Imagine you're tossing a baseball straight up in the air.

Let's try visualizing this with a height vs. Over time the ball goes up to a maximum height, and then back down to the starting height again when you catch it.

### Why is acceleration inversely proportional to mass? | Socratic

A parabola is a good indication of a quadratic relationship We can see our graph creates an upside-down parabola, which is the sort of thing you might expect from a quadratic relation. To make absolutely sure the relation between height and time is quadratic, we'll also look at the vertical equation for projectile motion that deals with position and time: Does it look familiar?

**Direct and inverse proportions(Direct proportion-01)**

Let's try rearranging the equation a bit: You might not know this yet, but in this equation the only two variables are height y and time t.