The displacement of a body is given by r=√(a^2-t^2)+tcos t^2, where a is constant. Find velocity?

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Answer 1 · 2018-05-11T12:18:44

#color(blue)(-t/((a^2-t^2)^(1/2))-2t^2sin(t^2)+cos(t^2)#

The change in displacement(distance) per unit of time is velocity.

Given:

#r=sqrt(a^2-t^2)+tcos(t^2)#

#"velocity"=(dr)/(dt)#

Rewriting as:

#r=(a^2-t^2)^(1/2)+tcos(t^2)#

#(dr)/(dt)((a^2-t^2)^(1/2)+tcos(t^2))=1/2(a^2-t^2)^(-1/2)*(-2t)+#

#->t(-sin(t^2)*(2t)+cos(t^2)#

#=(-2t)/(2(a^2-t^2)^(1/2))-2t^2sin(t^2)+cos(t^2)#

#=-t/((a^2-t^2)^(1/2))-2t^2sin(t^2)+cos(t^2)#