Question

A force \( \vec{F}=ai+bj+ck \) is acting on a body of mass \( m \). The body was initially at rest at the origin. The coordinates of the body after time \( t \) will be

• A. \( \left(\frac{at^2}{2m},\frac{bt^2}{2m},\frac{ct^2}{2m}\right) \)
• B. \( \left(\frac{at^2}{2m},\frac{bt^2}{m},\frac{ct^2}{2m}\right) \)
• C. \( \left(\frac{at^2}{m},\frac{bt^2}{2m},\frac{ct^2}{2m}\right) \)
• D. \( \left(\frac{at^2}{2m},\frac{bt^2}{2m},\frac{ct^2}{m}\right) \)

Hint:

Constant force motion: \begin{itemize} \item Use \( s=\frac12 at^2 \). \item Apply component-wise. \end{itemize}

Answer 1

The Correct Option is A

Concept: Newton's second law: \[ \vec{a}=\frac{\vec{F}}{m} \] Step 1: {\color{red}Acceleration components.} \[ a_x=\frac{a}{m},\quad a_y=\frac{b}{m},\quad a_z=\frac{c}{m} \] Step 2: {\color{red}Initial conditions.} Body starts from rest at origin. Displacement: \[ s=\frac{1}{2}at^2 \] Step 3: {\color{red}Coordinates.} \[ x=\frac{at^2}{2m},\quad y=\frac{bt^2}{2m},\quad z=\frac{ct^2}{2m} \]