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Position of a paricle along x axis is given by x=9t 2 -t 3 .What will be the position of the particle when it achieves maximum speed along psitive x direction?

Position of a paricle along x axis is given by x=9t2-t3.What will be the position of the particle when it achieves maximum speed along psitive x direction?

Grade:12th pass

2 Answers

Samyak
49 Points
6 years ago
To find speed we need to differentiate wrt time. v=18t-3t^2To find maxima we differentiate it again and equate to zero. Thus 18-9t=0t=2 secNow position at that instant is 9(2)^2-(2)^3=28m
DIWAKAR PANDEY
168 Points
6 years ago
We have to find Maxima of velocity so 1st get the equation of velocity from equation of x by differentiating it. dx/dt=v=18t-3t^2 Again differentiate it and put dv/dt=0=18-6t So. 18=6t So t=3s At 3 second velocity is maximum .Put this 3 second in equation of x because we have to calculate the "x"of body when "v" is Max. From here put t=3 s (9ร—3ร—3)-(3ร—3ร—3)=x X= 81-27 X=54

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