Question

select the correct answer.
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?

a. ( d_2 = v(t_2 - t_1) + d_1 )

b. ( d_1 = v(t_2 - t_1) - d_2 )

c. ( t_2 = v(d_2 - d_1) + t_1 )

d. ( t_1 = v(d_2 - d_1) - t_2 )

Explanation:

Step1: Start with the given formula

We have the formula for average velocity \( v=\frac{d_2 - d_1}{t_2 - t_1} \).

Step2: Multiply both sides by \( t_2 - t_1 \)

To eliminate the denominator, we multiply both sides of the equation by \( t_2 - t_1 \). This gives us \( v(t_2 - t_1)=d_2 - d_1 \).

Step3: Add \( d_1 \) to both sides

Now, we add \( d_1 \) to both sides of the equation \( v(t_2 - t_1)=d_2 - d_1 \) to solve for \( d_2 \). So, \( v(t_2 - t_1)+d_1=d_2 \), which can be rewritten as \( d_2 = v(t_2 - t_1)+d_1 \).

Answer:

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