Question

consider the formula for the average velocity, \\(v\\), of a moving particle. in the formula, \\(d_1\\) and \\(d_2\\) represent the distance traveled by the particle at times \\(t_1\\) and \\(t_2\\) respectively.

\\v = \frac{d_2 - d_1}{t_2 - t_1}\\

which of the following equations is equivalent to the formula for velocity?

\\(t_1 = v(d_2 - d_1) - t_2\\)

\\(t_2 = v(d_2 - d_1) + t_1\\)

\\(d_2 = v(t_2 - t_1) + d_1\\)

\\(d_1 = v(t_2 - t_1) - d_2\\)

Explanation:

Multiply both sides by the denominator

$$ v(t_2 - t_1) = d_2 - d_1 $$

Isolate the target variable

$$ d_2 = v(t_2 - t_1) + d_1 $$

Answer:

• (A) \(t_1 = v(d_2 - d_1) - t_2\)
• (B) \(t_2 = v(d_2 - d_1) + t_1\)</mcq-correct>
• (C) \(d_2 = v(t_2 - t_1) + d_1\) (Correct answer)

<mcq-option>(D) \(d_1 = v(t_2 - t_1) - d_2\)