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» Solution :From Eq . (4.34a) for `r_(0)=0`, the POSITION of the PARTICLE is given by `r(t)=v_(0)t+(1)/(2)at^(2)` `=5.0hati+(1//2)(3.0hati+2.0hatj)t^(2)` Therefore , `x(t)=5.0t+1.5t^(2)` `y(t)=+1.0t^(2)` Given`x(t)=84m.t=`? `5.0t+1.5t^(2)=84rArrt=6s` At`t=6s,y=1.0(6)^(2)=36.0m` Now , the velocity `v=(dr)/(dt)=(5.0+3.0)hati+2.0hatj` At `t=6s,v=23.0hati+12.0hatj` speed `=\|v\|=sqrt(23^(2)+12^(2))~=26 "m s"^(-1)`.