A particle leaves the origin with an initial velocity u=(3i^) and a constant acceleration a=(-1.0i^-0.5j^) m/s2. Its velocity v and position vector r when it reaches its maximum x coordinate are

ux=3m/s, ax=−1.0m/s2∴    vx2=ux2+2ax⋅x or     0=(3)2+2(−1)(x) or     x=4.5m Also vx=ux+axt 0=3−1.0t or t=3sy=uyt+12ayt2=0+12(−0.5)(3)2                         =−2.25m and vy=ayt=(−0.5)(3)=−1.5m/s∴ v=vxi^+vyj^=0−1.5j^=(−1.5j^)m/s and r=xi^+yj^=(4.5i^−2.25j^)m