A-particle-is-moving-in-parabolic-path-x-2-y-with-constant-speed-u-Find-the-acceleration-of-the-particle-when-it-crossess-origin-Also-find-the-radius-of-curvature-at-origin- Tinku Tara June 4, 2023 Others 0 Comments FacebookTweetPin Question Number 16499 by Tinkutara last updated on 23/Jun/17 Aparticleismovinginparabolicpathx2=y,withconstantspeedu.Findtheaccelerationoftheparticlewhenitcrossessorigin.Alsofindtheradiusofcurvatureatorigin. Answered by ajfour last updated on 23/Jun/17 x2=y⇒dydx=2xwhichiszeroattheorigin.Andd2ydx2=2radiusofcurvature,r=∣[1+(dy/dx)2]3/2d2y/dx2∣=12.x2=y2xdxdt=dydt=vy(=0atorigin)..(i)u2=(dxdt)2+(dydt)2….(ii)⇒(dxdt)2=u21+4x2….(iii)so(dxdt)2=u2attheorigin2(dxdt)2+2xd2xdt2=d2ydt2…..(iv)meansatorigin,d2ydt2=ay=2u2……(v)⇒(dxdt)2=u21+4x22(dxdt)(d2xdt2)=−8u2x(1+4x2)2(dxdt)ax=d2xdt2=−4u2x(1+4x2)2,thisiszeroattheorigin.accelerationa=d2xdt2+d2ydt2atorigina=0+2u2[see(v)]. Commented by Tinkutara last updated on 23/Jun/17 ThanksSir! Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Two-particles-are-revolving-on-two-coplanar-circles-with-constant-angular-velocities-1-and-2-respectively-Their-time-periods-are-T-1-and-T-2-then-prove-that-the-time-taken-by-second-particle-Next Next post: find-the-taylor-series-of-f-z-sinz-z-pi-4-in-complex-number- Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.