কাজ

A force F=(3ti^+5j^)\vec { F }=(3t\hat { i } +5\hat { j })N acts on a body due to which its position varies as S=(2t2i^5j^)\vec { S }=(2{t^2}\hat { i } -5\hat { j }). Find the work done by this force in initial 2s2s.

হানি নাটস

Given,

Force, F=(3ti^+5j^)NF=\left( 3t\hat{i}+5\hat{j} \right)N

Displacement, s=(2t2i^5j^)ms=\left( 2{{t}^{2}}\hat{i}-5\hat{j} \right)\,m

ds=(4ti^+0J^)dtds=\left( 4t\hat{i}+0\hat{J} \right)\,dt

dw=F.ds dw=F.ds

0wdw=02(3ti^+5j^)(4ti^+0j^)dt \int_{0}^{w}{dw}=\int_{0}^{2}{\left( 3t\hat{i}+5\hat{j} \right)}\left( 4t\hat{i}+0\hat{j} \right)\,dt

W=12t202=48J W=\left. 12{{t}^{2}} \right|_{0}^{2}=48\,J

Net work done is 48J48\,J

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