Question

How do you solve for $v$ in $s=vt?$

Answer 1

Hint: This is a linear equation. In mathematics, a linear equation is an equation that may be put in the form where are the variables, and are the coefficients, which are often real numbers. The coefficient may be considered as parameters of the equation, and may be arbitrary expressions, provided they do not contain any of the variables.

Complete step-by-step solution:
Given a linear equation with variables on both sides.
We have to solve for one variable which is the given equation.
The given equation is a distance formula equation, where the distance is the product of the velocity and time taken to complete the distance within a given velocity.
Here $s$ is the distance covered.
The variable $v$ stands for the velocity or speed .
The time taken is denoted by the variable $t$.
So the equation is given by:
$\Rightarrow s=vt$
Now the above equation is divided by $t$, as given below:
First consider the given equation.
$\Rightarrow s=vt$
$\Rightarrow {\displaystyle \frac{s}{t}}={\displaystyle \frac{vt}{t}}$
Now on the right hand side of the equation, $t$ gets cancelled on both the numerator and the denominator, which is given below:
$\Rightarrow {\displaystyle \frac{s}{t}}=v$
$\therefore v={\displaystyle \frac{s}{t}}$

The expression of $v$ is equal to ${\displaystyle \frac{s}{t}}$, which is $v={\displaystyle \frac{s}{t}}$.

Note: Please note that the linear equations of the first order. These equations are defined for lines in the coordinate system. An equation for a straight line is called a linear equation. The general representation of the straight-line equation is $y=mx+b$, where $m$ is the slope of the line and $b$is the y-intercept, here in the given equation $s=vt$, there is no intercept.