💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!
Get the answer to your homework problem.
Try Numerade Free for 7 Days
Like
Report
The equation of motion of a particle is $ = t^3 - 3t, $ where is in meters and is in seconds. Find(a) the velocity and acceleration as functions of $ t, $(b) the acceleration after $ 2 s, $ and(c) the acceleration when the velocity is 0.
(a) $$a(t)=v^{\prime}(t)=6 t$$(b) $$a(2)=6(2)=12 \mathrm{m} / \mathrm{s}^{2}$$(c) $$v(t)=3 t^{2}-3=0 \text { when } t^{2}=1, \text { that is, } t=1[t \geq 0] \text { and } a(1)=6 \mathrm{m} / \mathrm{s}^{2}$$
01:07
Frank L.
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 1
Derivatives of Polynomials and Exponential Functions
Derivatives
Differentiation
Missouri State University
University of Nottingham
Boston College
Lectures
03:09
In mathematics, precalculu…
31:55
In mathematics, a function…
02:28
The equation of motion of …
05:19
The acceleration function …
01:19
0:00
The velocity function (in …
01:23
Find the velocity and acce…
01:46
The acceleration of a part…
04:46
Find the velocity, acceler…
01:21
The position of a particle…
02:21
Hey, it's clear. So in Yuma, read here. So we're going to note that velocity is the derivative of the displacement. He s over DT, which is equal to de over de ti Pretty cute. Minus three T, which is equal to three. T square minus three and we need acceleration. And that's the derivative of velocity. Do you be over DT? That is therefore equal to 60. For part B, we have acceleration, which is equal to 60 to find it. After two seconds, we just have to plug in two for tea that becomes equal to 12 meters per second square. We're seeing we have our velocity equation, which is three t square minus three. We're gonna find out at what time? The velocities zero. So we're gonna plug in zero for B A and Saul for tea. We get T is equal to one. Now we just plug it into acceleration. We get six meters per second square
Numerade Educator
In mathematics, precalculus is the study of functions (as opposed to calculu…
In mathematics, a function (or map) f from a set X to a set Y is a rule whic…
The equation of motion of a particle is, $ s = 2t^4 - 2t^3 + t^2 - t $ , whe…
The acceleration function (in $ m/s^2 $) and the initial velocity are given …
The equation of motion of a particle is $s=2 t^{3}-7 t^{2}+4 t+1,$ where $s$…
The velocity function (in meters per second) is given for a particle moving …
Find the velocity and acceleration of a particle whose position function is …
The acceleration of a particle is defined by the relation $a=3 e^{-0.2 t},$ …
Find the velocity, acceleration, and speed of a particle with the given posi…
The position of a particle is $\overrightarrow{\mathbf{r}}(t)=\left(3.0 t^{2…
The position of a particle is given by the function $x=$ $\left(2 t^{3}-9 t^…
