Question

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

• A. \( \frac{ar^2}{2m} i + \frac{br^2}{2m} j + \frac{cr^2}{2m} k \)
• B. \( \frac{ar^2}{2m} i + \frac{br^2}{2m} j + \frac{cr^2}{2m} k \)
• C. \( \frac{ar}{m} i + \frac{br}{m} j + \frac{cr}{m} k \)
• D. \( \frac{ar}{m} i + \frac{br}{m} j + \frac{cr}{m} k \)

Hint:

To find the position vector in motion under a constant force, integrate the acceleration twice and apply the initial conditions such as rest at the origin.