Explanation:
It is given that, the position of a particle as as function of time t is given by :
[tex]r(t)=(8t+9)i+(2t^2-8)j+6tk[/tex]
Let v is the velocity of the particle. Velocity of an object is given by :
[tex]v=\dfrac{dr(t)}{dt}[/tex]
[tex]v=\dfrac{d[(8t+9)i+(2t^2-8)j+6tk]}{dt}[/tex]
[tex]v=(8i+4tj+6k)\ m/s[/tex]
So, the above equation is the velocity vector.
Let a is the acceleration of the particle. Acceleration of an object is given by :
[tex]a=\dfrac{dv(t)}{dt}[/tex]
[tex]a=\dfrac{d[8i+4tj+6k]}{dt}[/tex]
[tex]a=(4j)\ m/s^2[/tex]
At t = 0, [tex]v=(8i+0+6k)\ m/s[/tex]
[tex]v(t)=\sqrt{8^2+6^2} =10\ m/s[/tex]
Hence, this is the required solution.