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The position of of a particle is given b...

The position of of a particle is given by `vec r =3.0 t hat I + 2.0 t^(2) hat j+ 5.0 hat k` wher (t) in seconds and the coefficients mave the proper units for `ve r` to ber in metres. Find the velocity and acceleration of the particle in magnitude and direction at time `t=3.0 s`

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Velocity `vecv=(d(vecr))/(dt)=(3thati+2t^(2) hatj+5hatk)=3hati+4hatj`
Acceleration, `veca=(dvecv)/(dt)=0+4hatj=4hatj" when "t=3.0 s, vecv=3hati+4 xx 3hatj=3hati+12hatj`
`therefore v=sqrt(3^(2)+12^(2))=12.4ms^(-1)`
If is the angle which the direction of makes with the x-axis, then `tan theta=12/3=4 tan 76^@ or theta approx 76^@`
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