A body of mass 1 kg begins to move under the action of a time dependent force vec(F) =(2t hat(i)+3t^(2)hat(j)) N . Where hat(i) and hat(j) are unitvectors along X and Y axis . What power will be developed by the force at the time t .

A body of mass 1 kg begins to move under the action of a time dependen

1.	A body of mass 1 kg begins to move under the action of a time dependent force vec(F) =(2t hat(i)+3t^(2)hat(j)) N . Where hat(i) and hat(j) are unitvectors along X and Y axis . What power will be developed by the force at the time t .
Answer» `(2t^(2)+4t^(4))W` `(2t^(3)+3t^(4))W` `(2t^(3)+3t^(5))W` `(2t^(2)+3t^(3))W` Solution :`vec(F) =(2t hat(i)+3t hat(J))N ` and `vec(a) =(vec(F))/m = (2t hat(i)+3t^(2) hat(j))ms^(-2)` ` :. V = int_(0)^(t) "a dt"` ` = int_(0)^(t) (2t hat(i)+3t^(2)hat(j)) dt` ` = [ t^(2) hat(i) +t^(3) hat(j)]_(0)^(t)` `= t^(2) hat(i)+t^(3) hat(j)` ` :. ` Power `P = vec(F ) .vec(v)` ` = (2t hat(i) +3t^(2)hat(j)).(t^(2)hat(i)+t^(3)hat(j))` ` :. P = (2t^(3)+3t^(5))W`