What does the equation mean here? Y = f(t) = t^2 (where y = m and t = s)

[Indranil]

In distance vs time graph, Y = f(t) = t^2 (where y = m and t = s). Now my questions are as follows

1. From where has the ''t^2'' come? and how it has come?

2. What does the ''t^2'' mean here?

3. what is the relation between f(t) and t^2?

I am confused. Could you explain them, please?

 

[JeffM]

In distance vs time graph, Y = f(t) = t^2 (where y = m and t = s). Now my questions are as follows

1. From where has the ''t^2'' come? and how it has come?

2. What does the ''t^2'' mean here?

3. what is the relation between f(t) and t^2?

I am confused. Could you explain them, please?

First, \(\displaystyle t \text {^} 2 \equiv t^2 \equiv t * t.\)

Function notation. The notation f(t) = some formula means, in what is admittedly a simplification, that we will, for purposes of this problem or discussion, substitute f(t) for the formula. It is simply a different way to express the formula. The notation seems pointless with such a simple formula as t^2. But what if the formula was

\(\displaystyle f(t) = \dfrac{ln \left ( \dfrac{|sin (t)|}{\pi ^2} \right ) }{2^t}.\) Which is simpler to write?

Or what if you wanted to talk about a formula that you do not know yet or about formulas in general? Then f(t) just means some as yet unspecified formula in t.

To to evaluate f(3) for example you replace t in the formula with 3 and do the arithmetic. In graphing, it is traditional to graph the values of f(t) on the vertical (or "y") axis and the values of t on the horizontal (or "x") axis.

Finally, where did the formula come from? Who knows. They are telling you that, for this problem, this is the formula to use.

 

[Indranil]

First, \(\displaystyle t \text {^} 2 \equiv t^2 \equiv t * t.\)

Function notation. The notation f(t) = some formula means, in what is admittedly a simplification, that we will, for purposes of this problem or discussion, substitute f(t) for the formula. It is simply a different way to express the formula. The notation seems pointless with such a simple formula as t^2. But what if the formula was

\(\displaystyle f(t) = \dfrac{ln \left ( \dfrac{|sin (t)|}{\pi ^2} \right ) }{2^t}.\) Which is simpler to write?

Or what if you wanted to talk about a formula that you do not know yet or about formulas in general? Then f(t) just means some as yet unspecified formula in t.

To to evaluate f(3) for example you replace t in the formula with 3 and do the arithmetic. In graphing, it is traditional to graph the values of f(t) on the vertical (or "y") axis and the values of t on the horizontal (or "x") axis.

Finally, where did the formula come from? Who knows. They are telling you that, for this problem, this is the formula to use.

Thank you very much. I got it.