The position vector of a particle is given by r = 3 ,t^2 i + 2 ,t j + 5 , k . Which one of the following statements is correct?

Step-by-step solution

Given position vector r = 3 t^2 i + 2 t j + 5 k Velocity v = d r dt = 2 3 t i + 2 j Instantaneous momentum p = m v = m(2 3 t i + 2 j ) Acceleration a = d v dt = 2 3 i Force F = m a = 2 3 m i Taking the cross product of force and momentum: F p = (2 3 m i ) m(2 3 t i + 2 j ) = 2 6 m^2 k 0 Since the cross product is non-zero, the force is not parallel to the instantaneous momentum. Also, F p = 12m^2t 0 , so they are not perpendicular either. Answer: The force acting on the particle is not parallel to the instantaneous