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The coordinate of a moving point at time t are given by x = a ( 2t + sin 2t) , y = a ( 1-cos 2t). Prove that acceleration is constant. |
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Answer» x=a(2t+sin2t) `dx/dt=2a+a-cos2t*2` `d^x/dt=0+2a-sin2x2i` `=-4asin2thati` `dy/dt=asin2t*2` `d^y/dt^2=2a*2cos2t` `=4acos2thatj` `|veca|=sqrt(a_x^2+a_y^2)` `=sqrt(16a^2sin^2t+16a^2cos^2 2t)` `=sqrt(16a^2)` =4a. |
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