What force is required so that a particle of mass m has the position function r(t) = t3 i + 8t2 j + t3 k?

Explanation:

Given

Position of Particle is given by

Velocity is given by

acceleration is given by

Force is given by

F= m ( 6 t i + 18 j  + 6 t k)

Explanation:

 Given that

mass of the particle =m

The position of the particle

r=t³ i + 8 t² j +t³ k

We know that velocity of the particle is given as

v=3  t² i + 18 t j +3  t² k

Now the acceleration of the particle

a= 6 t i + 18 j  + 6 t k

Therefore the force F

F= m a

F= m ( 6 t i + 18 j  + 6 t k)

The force required will be

F= m ( 6 t i + 18 j  + 6 t k)

unlike poles attract