Instantaneous Acceleration in 2D Video Lessons

Concept

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

92% (459 ratings)
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 =

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Instantaneous Acceleration in 2D concept. You can view video lessons to learn Instantaneous Acceleration in 2D. Or if you need more Instantaneous Acceleration in 2D practice, you can also practice Instantaneous Acceleration in 2D practice problems.