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