A particle leaves the origin with an initial velodty `v= (3.00 hati) m//s` and a constant acceleration `a= (-1.00 hati-0.500 hatj) m//s^2.` When the particle reaches its maximum x coordinate, what are
(a) its velocity and (b) its position vector?

Answer

A, B, D

Explanation

(a) `u_x=3 m//s`
`a_x=-1.0 m//s^2`
Maximum x-coordinate is attained after time
`t=|(u_x)/(a_x)|=3s`
At this instant `v_x=0` and
`v_y=u_y+a_yt=0-0.5xx3=-1.5 m//s`
`:. v=(-1.5 hatj)m//s`
(b) `x=u_xt+1/2a_xt^2`
`=3xx3+1/2(-1.0)(3)^2=4.5 m`
`y=u_yt+1/2a_yt^2=0-1/2(0.5)(3)^2=-2.25 m`
`:. r=(4.5 hati-2.25 hatj)m`