Question

一质点沿曲线x=0,y=t,z=t^2,从点(0,0,0)移动到点(0,1,1)，求在此过程中，力F=根号1+x*向量i-y*向量j+向量K

题目如图所示
上图错的，这个才是准确的

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Answer 1

　　The velocity of the particle is v = (0,1,2t), where t belongs to [0,1]. F can be expressed as (0,-t,1). So the power of F at the time instance t is P(t) = F times v = 0 - t + 2t = t. Then work of F is the integration of P(t) = t over [0,1], that is 1/2 ( you can do the math yourself).