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The position of a particle is given by r...

The position of a particle is given by `r=3.0thati+2.0t^(2)hatj+5.0 hatk`. Where t is in seconds and the coefficients hav the proper units for r to be in matres. (a) find v(t) and a(t) of the particle (b). Find the magnijtude of direction of v(t) or t=1.0 s

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`v(t)(dr)/(dt)=(d)/(t)(3.0that(i)+2.0t^(2)hat(j)+5.0hat(k)) = 3.0hat(i)+4.0that(j)`
` a(t)=(dv)/(dt)=+4.0hat(j)`
`a = 4.0 m s^(-2)` along y direction
(b) `At t=1.0s, v=3.0hat(i)+4.0hat(j)`
It.s magnitude is `v=sqrt(3^(2)+4^(2))=5.0ms^(-1)` and direction is
`theta = tan^(-1)((v_(y))/(v_(x)))=tan^(-1)((4)/(3))=53^(0)` with x-axis.
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