Question

Consider the equation ∆x = v0t + (1/2)at2. What is the variable a equal to?

Answer 1

Given the equation:

$\Delta x=v_0t+\frac{1}{2}at^2$

Let's determine what the variable ''a'' represents.

The given equation can be called the motion equation.

We have the variables below:

• x represents the displacement of the object

,

• v0 represents the velocity of the object.

,

• a represents the acceleration.

,

• t represents the time.

Let's rewrite the equation for a.

Rearrange the equation:

$v_ot+\frac{1}{2}at^2=\Delta x$

Subtract vot from both sides:

$\begin{gathered} v_0t-v_0t+\frac{1}{2}at^2=\Delta x-v_0t \\ \\ \frac{1}{2}at^2=\Delta x-v_0t \end{gathered}$

Now, Multiply all terms by 2:

$\begin{gathered} 2*\frac{1}{2}at^2=2(\Delta x-v_0t) \\ \\ at^2=2(\Delta x-v_0t) \end{gathered}$

Divide both sides by t^2:

$\begin{gathered} \frac{at^2}{t^2}=\frac{2(\Delta x-v_0t)}{t^2} \\ \\ a=\frac{2(\Delta x-v_{0t})}{t^2} \end{gathered}$

Therefore, the variable a is equal to:

2(Δx - v₀t)/t²

ANSWER:

2(Δx - v₀t)/t²