Instantaneous Acceleration in 2D Video Lessons

Concept

# Problem: A particle moving in the xy-plane has velocity v =(2ti+(3−t2)j) m/s, where t is in s.Part AWhat is the x component of the particle's acceleration vector at t = 6 s?Express your answer with the appropriate units.Part BWhat is the y component of the particle's acceleration vector at t = 6 s?Express your answer with the appropriate units.

###### FREE Expert Solution

Acceleration a:

$\overline{)\stackrel{\mathbf{⇀}}{\mathbit{a}}{\mathbf{\left(}}{\mathbit{t}}{\mathbf{\right)}}{\mathbf{=}}\frac{\mathbit{d}\stackrel{\mathbf{⇀}}{\mathbit{v}}\mathbf{\left(}\mathbit{t}\mathbf{\right)}}{\mathbit{d}\mathbit{t}}}$

Power rule of differentiation:

$\overline{)\frac{\mathbit{d}}{\mathbit{d}\mathbit{t}}\mathbf{\left(}{\mathbit{x}}^{\mathbit{n}}\mathbf{\right)}{\mathbf{=}}{\mathbit{n}}{{\mathbit{x}}}^{\mathbit{n}\mathbf{-}\mathbf{1}}}$

###### Problem Details

A particle moving in the xy-plane has velocity v =(2ti+(3−t2)j) m/s, where t is in s.

Part A

What is the x component of the particle's acceleration vector at t = 6 s?

Part B

What is the y component of the particle's acceleration vector at t = 6 s?