Question

if S = at² + bt + c, where S is the distance, and t is the time, find the correct unit of a, b and c​

Answer 1

Answer:

$a$ is in units of $\frac{m}{s^{2}}$

$b$ is in units of $\frac{m}{s}$

$c$ is in units of $m$

Explanation:

We have the following expression:

$S=at^{2}+bt+c$

Where:

$S$ is the distance, hence its unit is $m$ (meters, assuming we are using the International System of Units)

$t$ is the time, hence its unit is $s$ (seconds)

So, the expression is rewritten as:

$m=as^{2}+bs+c$

Since the left side of the equation is in meters, the right side must be in meters as well.

In addition, in the right side we have terms that have to added, this means each term must be in meters:

- For the first term $a$ must be in units of $\frac{m}{s^{2}}$ in order to have meters.

- For the second term $b$ must be in units of $\frac{m}{s}$ in order to have meters.

- For the third term $c$ must be in units of $m$ in order to have meters.