A particle stars from origin at t=0 with a velocity 5.0hatim//s and moves in x-y plane under action of a force which produces a constant acceleration of (3.0hati+2.0hatj) m//s^(2). (a)What is the y- coordinate of the particle at the instant its x - coordinate is 84 m ? (b) What is the speed of the particle at this time ?

A particle stars from origin at t=0 with a velocity 5.0hatim//s and mo

1.	A particle stars from origin at t=0 with a velocity 5.0hatim//s and moves in x-y plane under action of a force which produces a constant acceleration of (3.0hati+2.0hatj) m//s^(2). (a)What is the y- coordinate of the particle at the instant its x - coordinate is 84 m ? (b) What is the speed of the particle at this time ?
Answer» <html><body><p></p>Solution :From Eq . (4.34a) for `r_(0)=0`, the <a href="https://interviewquestions.tuteehub.com/tag/position-1159826" style="font-weight:bold;" target="_blank" title="Click to know more about POSITION">POSITION</a> of the <a href="https://interviewquestions.tuteehub.com/tag/particle-1147478" style="font-weight:bold;" target="_blank" title="Click to know more about PARTICLE">PARTICLE</a> is given by `r(t)=v_(0)t+(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)/(2)at^(2)`<br/>`=5.0hati+(1//2)(3.0hati+2.0hatj)t^(2)`<br/>Therefore , `x(t)=5.0t+1.5t^(2)`<br/>`y(t)=+1.0t^(2)`<br/>Given`x(t)=84m.t=`?<br/>`5.0t+1.5t^(2)=84rArrt=6s`<br/>At`t=6s,y=1.0(6)^(2)=36.0m`<br/>Now , the velocity `v=(dr)/(dt)=(5.0+3.0)hati+2.0hatj`<br/>At `t=6s,v=23.0hati+12.0hatj`<br/>speed `=\|v\|=sqrt(23^(2)+12^(2))~=<a href="https://interviewquestions.tuteehub.com/tag/26-298265" style="font-weight:bold;" target="_blank" title="Click to know more about 26">26</a> "m s"^(-1)`.</body></html>