A particle is at rest at the origin. A force A→$$=(ai^+bj^+6k^)N$$ is applied on the particle and it is displaced from the origin to the point (1$$, $$2$$, $$3) metre. For what values of ‘a’ and ‘b’, the particle will gain maximum kinetic energy?

Question

A particle is at rest at the origin. A force A→$$=(ai^+bj^+6k^)N$$ is applied on the particle and it is displaced from the origin to the point (1$$, $$2$$, $$3) metre. For what values of ‘a’ and ‘b’, the particle will gain maximum kinetic energy?

Infinity Learn · Accepted Answer

displacement, d→$$=(i^+2j^+3k^)mW=F$$→.d→$$=Fdcos$$⁡θBy $$work-energy$$ theorem kinetic energy gained will be maximum, work done on the particle is maximum i.e., when θ$$=0o$$.i.e. when F→ and d→ are parallel. In that case, $$a1=b2=c3$$⇒$$a=2$$ and $$b=4$$

A particle is at rest at the origin. A force $\vec{A} = (a \hat{i} + b \hat{j} + 6 \hat{k}) N$ is applied on the particle and it is displaced from the origin to the point (1, 2, 3) metre. For what values of ‘a’ and ‘b’, the particle will gain maximum kinetic energy?

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

A particle is at rest at the origin. A force A→=(ai^+bj^+6k^)N is applied on the particle and it is displaced from the origin to the point (1, 2, 3) metre. For what values of ‘a’ and ‘b’, the particle will gain maximum kinetic energy?

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

A particle is at rest at the origin. A force $\vec{A} = (a \hat{i} + b \hat{j} + 6 \hat{k}) N$ is applied on the particle and it is displaced from the origin to the point (1, 2, 3) metre. For what values of ‘a’ and ‘b’, the particle will gain maximum kinetic energy?