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

The position of a particle is given by `vecr=(8thati+3t^(2)hatj+5hatk)m` where t is measured in second and `vecr` in meter. Calculate, the velocity and the acceleration of the particle.

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To solve the problem, we need to calculate the velocity and acceleration of the particle given its position vector \(\vec{r} = (8t \hat{i} + 3t^2 \hat{j} + 5 \hat{k})\) meters. ### Step 1: Calculate the Velocity Vector The velocity vector \(\vec{v}\) is defined as the rate of change of the position vector \(\vec{r}\) with respect to time \(t\). Mathematically, this is expressed as: \[ \vec{v} = \frac{d\vec{r}}{dt} \] ...
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