# Problem: A particle's trajectory is described by x =(12t3−2t2)m and y =(12t2−2t)m, where t is in s.Part C What is the particle's direction of motion, measured as an angle from the x-axis, at t=0 s ? Express your answer using two significant figures. θ =

###### FREE Expert Solution

Part C

Direction θ = tan-1(vy/vx)

The x-component of velocity, vx at t = 0s

$\begin{array}{rcl}{\mathbf{v}}_{\mathbf{x}}& \mathbf{=}& \frac{\mathbf{d}\mathbf{x}}{\mathbf{d}\mathbf{t}}\\ & \mathbf{=}& \frac{\mathbf{d}}{\mathbf{d}\mathbf{t}}\mathbf{\left(}\mathbf{12}{\mathbf{t}}^{\mathbf{3}}\mathbf{-}\mathbf{2}{\mathbf{t}}^{\mathbf{2}}\mathbf{\right)}\end{array}$

vx = 36t2 - 4t = (36)(0)2 - 4(0) = 0 m/s.

The y-component of velocity, vy at t = 0 s

###### Problem Details

A particle's trajectory is described by x =(12t3−2t2)m and y =(12t2−2t)m, where t is in s.

Part C What is the particle's direction of motion, measured as an angle from the x-axis, at t=0 s ? Express your answer using two significant figures. θ =