Answer:
The particle's velocity is the derivative of the particle's position. The particles's acceleration is the derivative of the particle's velocity. You can compute the velocity and acceleration as follows:
Step-by-step explanation:
![\vec{v}(t)=\frac{dr}{dt}=\frac{d}{dt}(8t+5)\overrightarrow{i}+\frac{d}{dt}(8t^2-2)\overrightarrow{j}+\frac{d}{dt}(6t)\overrightarrow{k}=8\overrightarrow{i}+16t\overrightarrow{j}+6\overrightarrow{k}.](https://tex.z-dn.net/?f=%5Cvec%7Bv%7D%28t%29%3D%5Cfrac%7Bdr%7D%7Bdt%7D%3D%5Cfrac%7Bd%7D%7Bdt%7D%288t%2B5%29%5Coverrightarrow%7Bi%7D%2B%5Cfrac%7Bd%7D%7Bdt%7D%288t%5E2-2%29%5Coverrightarrow%7Bj%7D%2B%5Cfrac%7Bd%7D%7Bdt%7D%286t%29%5Coverrightarrow%7Bk%7D%3D8%5Coverrightarrow%7Bi%7D%2B16t%5Coverrightarrow%7Bj%7D%2B6%5Coverrightarrow%7Bk%7D.)
![\vec{a}(t)=\frac{dv}{dt}=\frac{d}{dt}(8)\overrightarrow{i}+\frac{d}{dt}(16t)\overrightarrow{j}+\frac{d}{dt}(6)\overrightarrow{k}=0\overrightarrow{i}+16\overrightarrow{j}+0\overrrighatarrow{k}.](https://tex.z-dn.net/?f=%5Cvec%7Ba%7D%28t%29%3D%5Cfrac%7Bdv%7D%7Bdt%7D%3D%5Cfrac%7Bd%7D%7Bdt%7D%288%29%5Coverrightarrow%7Bi%7D%2B%5Cfrac%7Bd%7D%7Bdt%7D%2816t%29%5Coverrightarrow%7Bj%7D%2B%5Cfrac%7Bd%7D%7Bdt%7D%286%29%5Coverrightarrow%7Bk%7D%3D0%5Coverrightarrow%7Bi%7D%2B16%5Coverrightarrow%7Bj%7D%2B0%5Coverrrighatarrow%7Bk%7D.)
The velocity at
is
.
The speed at t=0 is
. Then, the velocity at t=0 written as a product of the speed at t=0 and the direction at t=0 is
![\vec{v}(0)=\lVert \vec{v}(0)\rVert \dfrac{\vec{v}(0)}{\lVert \vec{v}(0)\rVert}=10\cdot(\dfrac{8}{10},0,\dfrac{6}{10}).](https://tex.z-dn.net/?f=%5Cvec%7Bv%7D%280%29%3D%5ClVert%20%5Cvec%7Bv%7D%280%29%5CrVert%20%5Cdfrac%7B%5Cvec%7Bv%7D%280%29%7D%7B%5ClVert%20%5Cvec%7Bv%7D%280%29%5CrVert%7D%3D10%5Ccdot%28%5Cdfrac%7B8%7D%7B10%7D%2C0%2C%5Cdfrac%7B6%7D%7B10%7D%29.)
Answer:
lie on goes
Step-by-step explanation:
8x+20=3x+45
5x+20=45
5x=25
x=5
Step-by-step explanation:
mx+b=y
mx=y-b
x=y-b/m
4-32
5-40
6-48
hope this helps!