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An object has a displacement from positi...

An object has a displacement from position vector `vec(r )_(1)=(2hat(i)+3hat(j))m` to `vec(r )_(2)=(4hat(i)+6hat(j))m` under a force `vec(F)=(3x^(2)hat(i)+2y hat(j))N`. Find the work done by this force.

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To find the work done by the force \(\vec{F} = (3x^2 \hat{i} + 2y \hat{j})\) as an object moves from position vector \(\vec{r}_1 = (2 \hat{i} + 3 \hat{j})\) m to \(\vec{r}_2 = (4 \hat{i} + 6 \hat{j})\) m, we can follow these steps: ### Step 1: Determine the displacement vector The displacement vector \(\vec{dr}\) can be expressed in terms of its components: \[ \vec{dr} = dx \hat{i} + dy \hat{j} \] ...
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