Chapter 3, Problem 7STP

To determine

To Choose: The correct option.

Answer to Problem 7STP

Option D. $\frac{v_f^2-v_i^2}{2x}$

Explanation of Solution

Introduction:

Final velocity with constant acceleration can be obtained using third equation of motion:

  $v^2{}_f=v^2{}_i+2a\left(d_f-d_i\right)$

Where, $v_f$ is the final velocity, $v_i$ is the initial velocity, a is the acceleration, $d_f$ is the final displacement and $d_i$ is the initial displacement.

Consider $d_f-d_i=x$ , then above formula can be written as:

  $v_f^2=v_i^2+2ax$

Subtracting $v_i^2$ from both sides of above equation:

  $\begin{array}{l}{v}_f^2-v_i^2=0+2ax\\ \Rightarrow a=\frac{v_f^2-v_i^2}{2x}\end{array}$

Conclusion:

Hence, the correct formula manipulation of the formula $v_f^2=v_i^2+2ax$ for the acceleration is $a=\frac{v_f^2-v_i^2}{2x}$ .