Let's solve the equation step by step.

Given equation:

\[ 10a_2t_2 = -3v_2 + \frac{2x_2}{t_2} \]

We want to isolate \( a_2 \), \( t_2 \), \( v_2 \), or \( x_2 \) depending on the variable of interest. Let's start by isolating \( a_2 \):

### Step 1: Divide both sides by \( t_2 \) to solve for \( a_2 \):

\[
10a_2 = \frac{-3v_2}{t_2} + \frac{2x_2}{t_2^2}
\]

### Step 2: Isolate \( a_2 \):

\[
a_2 = \frac{-3v_2}{10t_2} + \frac{2x_2}{10t_2^2}
\]

So the expression for \( a_2 \) is:

\[
a_2 = \frac{-3v_2}{10t_2} + \frac{x_2}{5t_2^2}
\]

This equation expresses \( a_2 \) in terms of \( v_2 \), \( t_2 \), and \( x_2 \).

Would you like more details or have any questions?

### Related Questions:
1. How can we isolate \( v_2 \) in the original equation?
2. What happens if \( t_2 = 0 \)? How does it affect the equation?
3. Can we solve this equation for \( t_2 \) explicitly?
4. What are the physical interpretations of \( a_2 \), \( v_2 \), \( t_2 \), and \( x_2 \) in this context?
5. How would the equation change if there was an additional term on either side?

### Tip:
Always check if the variables or constants in your equations can be factored or simplified before starting the isolation process.

Learn how to isolate variables in equations with a step-by-step solution for 10a2t2 = -3v2 + 2(x2/t2). Understand the process to solve for a2 in terms of v2, t2, and x2. Suitable for high school students studying algebraic manipulation.

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