Question

#3: solve the formula ( d = \frac{v_0 + v_f}{2} t ) relating to the translational motion, where ( d ) represents distance, ( v_0 ) represents initial velocity, ( v_f ) represents final velocity, and ( t ) represents time. rearrange the formula to isolate final velocity.

Explanation:

Step1: Start with the given formula

The formula is \( d=\frac{v_0 + v_f}{2}t \). Our goal is to isolate \( v_f \). First, multiply both sides by 2 to eliminate the denominator.
\( 2d=(v_0 + v_f)t \)

Step2: Divide both sides by t

To get rid of the \( t \) on the right - hand side, divide both sides of the equation by \( t \) (assuming \( t
eq0 \)).
\( \frac{2d}{t}=v_0 + v_f \)

Step3: Subtract \( v_0 \) from both sides

Now, to isolate \( v_f \), subtract \( v_0 \) from both sides of the equation.
\( v_f=\frac{2d}{t}-v_0 \)

Answer:

\( v_f=\frac{2d}{t}-v_0 \)