Velocity:

$\overline{){\mathbf{v}}{\mathbf{=}}\sqrt{{{\mathbf{v}}_{\mathbf{x}}}^{\mathbf{2}}\mathbf{+}{{\mathbf{v}}_{\mathbf{y}}}^{\mathbf{2}}}}$

The x-component of velocity, v_{x}

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

v_{x} = 36t^{2} - 4t

The y-component of velocity, v_{y}

$\begin{array}{rcl}{\mathbf{v}}_{\mathbf{y}}& \mathbf{=}& \frac{\mathbf{dy}}{\mathbf{dt}}\\ & \mathbf{=}& \frac{\mathbf{d}}{\mathbf{dt}}\mathbf{(}\mathbf{12}{\mathbf{t}}^{\mathbf{2}}\mathbf{-}\mathbf{2}\mathbf{t}\mathbf{)}\end{array}$

v_{y}_{ }= 24t - 2

A particle's trajectory is described by x =(12t^{3}−2t^{2})m and y =(12t^{2}−2t)m, where t is in s.

Part A What is the particle's speed at t=0s ? v = m/s

Frequently Asked Questions

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.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Walker's class at OSU.