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$t$ and $s(t)$ are physical quantitities. Quoted from Wikipedia:

A physical quantity can be expressed as a value, which is the algebraic multiplication of a numerical value and a unit of measurement.

Your equation $$s(t) = 2t^3 - 14t^2 + 20t - 44$$ is not correct to begin with. $s(t)$ is a length (having unit $\text{m}$) and $t$ is a time (having unit $\text{s}$). Hence the equation above is dimensionally inconsistent.

You make it dimensionally consistent by writing $$s(t) = 2\frac{\text{m}}{\text{s}^3}\ t^3 - 14\frac{\text{m}}{\text{s}^2}\ t^2 + 20\frac{\text{m}}{\text{s}}\ t - 44\text{ m}$$

When you now insert a value for $t$ with unit $\text{s}$ (for example $t=4.2\text{ s}$), you see the $\text{s}^3$, $\text{s}^2$ and $\text{s}$ in the terms on the right side all cancel out, and you finally get a number with unit $\text{m}$ which matches the unit of $s(t)$ on the left side.

$t$ and $s(t)$ are physical quantitities. Quoted from Wikipedia:

A physical quantity can be expressed as a value, which is the algebraic multiplication of a numerical value and a unit of measurement.

Your equation $$s(t) = 2t^3 - 14t^2 + 20t - 44$$ is not correct to begin with. $s(t)$ is a length (having unit $\text{m}$) and $t$ is a time (having unit $\text{s}$). Hence the equation above is dimensionally inhomogeneous.

You make it dimensionally homogeneous by writing $$s(t) = 2\frac{\text{m}}{\text{s}^3}\ t^3 - 14\frac{\text{m}}{\text{s}^2}\ t^2 + 20\frac{\text{m}}{\text{s}}\ t - 44\text{ m}$$

When you now insert a value for $t$ with unit $\text{s}$ (for example $t=4.2\text{ s}$), you see the $\text{s}^3$, $\text{s}^2$ and $\text{s}$ in the terms on the right side all cancel out, and you finally get a number with unit $\text{m}$ which matches the unit of $s(t)$ on the left side.

Your equation $$s(t) = 2t^3 - 14t^2 + 20t - 44$$ is not correct to begin with. $s(t)$ is a length (having unit $\text{m}$) and $t$ is a time (having unit $\text{s}$). Hence the equation above is dimensionally inconsistent.

You make it dimensionally consistent by writing $$s(t) = 2\frac{\text{m}}{\text{s}^3}\ t^3 - 14\frac{\text{m}}{\text{s}^2}\ t^2 + 20\frac{\text{m}}{\text{s}}\ t - 44\text{ m}$$

When you now insert a value for $t$ with unit $\text{s}$ (for example $t=4.2\text{ s}$), you see the $\text{s}^3$, $\text{s}^2$ and $\text{s}$ in the terms on the right side all cancel out, and you finally get a number with unit $\text{m}$ which matches the unit of $s(t)$ on the left side.

$t$ and $s(t)$ are physical quantitities. Quoted from Wikipedia:

A physical quantity can be expressed as a value, which is the algebraic multiplication of a numerical value and a unit of measurement.

Your equation $$s(t) = 2t^3 - 14t^2 + 20t - 44$$ is not correct to begin with. $s(t)$ is a length (having unit $\text{m}$) and $t$ is a time (having unit $\text{s}$). Hence the equation above is dimensionally inconsistent.

You make it dimensionally consistent by writing $$s(t) = 2\frac{\text{m}}{\text{s}^3}\ t^3 - 14\frac{\text{m}}{\text{s}^2}\ t^2 + 20\frac{\text{m}}{\text{s}}\ t - 44\text{ m}$$

When you now insert a value for $t$ with unit $\text{s}$ (for example $t=4.2\text{ s}$), you see the $\text{s}^3$, $\text{s}^2$ and $\text{s}$ in the terms on the right side all cancel out, and you finally get a number with unit $\text{m}$ which matches the unit of $s(t)$ on the left side.

Your equation $$s(t) = 2t^3 - 14t^2 + 20t - 44$$ is not correct to begin with. $s(t)$ is a length (having unit $\text{m}$) and $t$ is a time (having unit $\text{s}$). Hence the equation above is dimensionally inconsistent.

You make it dimensionally consistent by writing $$s(t) = 2\frac{\text{m}}{\text{s}^3}\ t^3 - 14\frac{\text{m}}{\text{s}^2}\ t^2 + 20\frac{\text{m}}{\text{s}}\ t - 44\text{ m}$$

When you now insert a value for $t$ with unit $\text{s}$, you see the $\text{s}^3$, $\text{s}^2$ and $\text{s}$ in the terms on the right side all cancel out, and you finally get a number with unit $\text{m}$ which matches the unit of $s(t)$ on the left side.

Your equation $$s(t) = 2t^3 - 14t^2 + 20t - 44$$ is not correct to begin with. $s(t)$ is a length (having unit $\text{m}$) and $t$ is a time (having unit $\text{s}$). Hence the equation above is dimensionally inconsistent.

You make it dimensionally consistent by writing $$s(t) = 2\frac{\text{m}}{\text{s}^3}\ t^3 - 14\frac{\text{m}}{\text{s}^2}\ t^2 + 20\frac{\text{m}}{\text{s}}\ t - 44\text{ m}$$

When you now insert a value for $t$ with unit $\text{s}$ (for example $t=4.2\text{ s}$), you see the $\text{s}^3$, $\text{s}^2$ and $\text{s}$ in the terms on the right side all cancel out, and you finally get a number with unit $\text{m}$ which matches the unit of $s(t)$ on the left side.