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The position vector of a particle is giv...

The position vector of a particle is given by `vec(r)=1.2 t hat(i)+0.9 t^(2) hat(j)-0.6(t^(3)-1)hat(k)` where t is the time in seconds from the start of motion and where `vec(r)` is expressed in meters. For the condition when `t=4` second, determine the power `(P=vec(F).vec(v))` in watts produced by the force `vec(F)=(60hat(i)-25hat(j)-40hat(k)) N` which is acting on the particle.

Text Solution

Verified by Experts

The correct Answer is:
1044
`vec(v)=(dvec(r))/(dt)=1.2 hat(i)+1.8that(j)-1.8t^(2)hat(k)`
at `t=4s, vec(v)=1.2 hat(i)+7.2 hat(j)-28.8 hat(k)`
`P=vec(F).vec(v)=(60hat(i)-25hat(j)-40hat(k)).(1.2hat(i)+7.2hat(j)-28.8hat(k))`
`=1044W`
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