The position vector of a particle is given by ? = 13t21 + 2t }+ 15k. Which one of the following statements is correct?

To determine the relationship between force and momentum, we analyze the position vector r = 13t2i + 2tj + 15k (interpreting the typographical errors in the original text):

• Velocity (v): Differentiating r with respect to time (t), we get v = dr/dt = 26ti + 2j.
• Momentum (p): Since p = mv, the instantaneous momentum is p = 26mti + 2mj.
• Acceleration (a): Differentiating v, we get a = dv/dt = 26i.
• Force (F): Using Newton's Second Law (F = ma), the force is F = 26mi.

The force F acts only along the x-axis (i). However, the momentum p has components along both the x-axis (26mti) and the y-axis (2mj). Because p is not a scalar multiple of F, the force is not parallel to the momentum. Thus, option D is correct.