Respuesta :
Answer:
Explanation:
Given
Position of Particle is given by
[tex]r(t)=t^3\hat{i}+\8t^2\hat{j}+t^3\hat{k}[/tex]
Velocity is given by
[tex]\frac{\mathrm{d} r(t)}{\mathrm{d} t}=v(t)[/tex]
[tex]v(t)=3t^2\hat{i}+\16t\hat{j}+3t^2\hat{k}[/tex]
acceleration is given by
[tex]a(t)=\frac{\mathrm{d} v}{\mathrm{d} t}[/tex]
[tex]a(t)=6t\hat{i}+\16\hat{j}+6t\hat{k}[/tex]
Force is given by
[tex]F=m\times a[/tex]
[tex]F=m\cdot \left ( 6t\hat{i}+\16\hat{j}+6t\hat{k}\right )[/tex]
Answer:
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
[tex]v=\dfrac{dr}{dt}[/tex]
v=3 t² i + 18 t j +3 t² k
Now the acceleration of the particle
[tex]a=\dfrac{dv}{dt}[/tex]
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)
