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A particle passes a fixed point O with a velocity of 20 m/s and moves in a straight line with an acceleration of 1/4 t m/s², where t is the time in seconds after passing through O.(a)Find the velocity function and the displacement function of the particle.(b)Calculate its distance traveled during the first... 顯示更多 A particle passes a fixed point O with a velocity of 20 m/s and moves in a straight line with an acceleration of 1/4 t m/s2, where t is the time in seconds after passing through O. (a)Find the velocity function and the displacement function of the particle. (b)Calculate its distance traveled during the first 6 seconds
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A particle passes a fixed point O with a velocity of 20 m/s and moves in a straight line with an acceleration of 1/4 t m/s2, where t is the time in seconds after passing through O. (a)Find the velocity function and the displacement function of the particle. acceleration A= 1/4 t velocity V=∫( 1/4 t)dt V=(1/8) t^2 +C when t=0, V=20,so 20=(1/8)( 0)^2 +C C=20 V=(1/8) t^2 +20 displacement D=∫[(1/8) t^2 +20]dt D=(1/24) t^3 +20t +C when t=0, D=0, so D=(1/24) t^3 +20t (b)Calculate its distance traveled during the first 6 seconds when t=6, D=(1/24) (6)^3 +20(6) =(1/24) (6)^3 +20(6) =129
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