Question

Using the equation x = x_0 + vt, where x_0 = 7.8, v = 4.1, and x =-9.8, what is the value of t?

Answer 1

Solving an Equation

When we're given an equation with one unknown, our goal is to isolate that variable to one side of the equal sign.

We can do this by performing inverse operations on both sides of the equal sign and canceling values out.

For instance, the inverse operation of addition is subtraction, and the inverse operation of division is multiplication.

Solving the Question

We're given:

• $x = x_0 + vt$
• $x_0 = 7.8\\v = 4.1\\ x =-9.8$

We have to solve for the value of t. Before we plug in the given values, we can begin by isolating t in the given equation:

$x = x_0 + vt$

First, subtract $x_0$ from both sides:

$x-x_0 = x_0 + vt-x_0\\x-x_0 =vt$

Now, divide both sides by v:

$\dfrac{x-x_0}{v} =\dfrac{vt}{v}\\\\\dfrac{x-x_0}{v} =t\\\\t=\dfrac{x-x_0}{v}$

Now, we have successfully isolated t.

Plug in all the given values:

$t=\dfrac{x-x_0}{v}$

$t=\dfrac{-17.6}{4.1}\\\\t=\dfrac{-176}{41}$

Answer

$t=\dfrac{-176}{41}$