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In a moving block, a variable force pushes it. Friction is acting against the movement.

Below equation specify the amount of energy could be used to give motion: $$ E_1 = \int F_T(t) .v(t) .dt $$

However, because of friction,energy used to give motion gets smaller:

$$ E_2= \int [F_T(t)-F_R].v(t).dt $$

Can I assume E2 as energy used to give motion and E3 as dissipated energy due to the friction? $$ E_3=\int F_R(t).v(t).dt $$

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Assuming you mean $F_R$ to be the frictional force then yes you can split up the energy as you suggest. Your $E_2$ will be the change in the kinetic energy of the object and the $E_3$ will be the energy lost due to friction.

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