Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Find the acceleration of an object for which the displacement $s$ (in $\mathrm{m}$ ) is given as a function of the time $t$ (in s) for the given value of $t.$$$s=\frac{16}{0.5 t^{2}+1}, t=2 \mathrm{s}$$

Calculus 1 / AB

Chapter 23

The Derivative

Section 9

Higher Derivatives

Derivatives

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

02:46

The position of an object …

01:45

Find the velocity and acce…

03:21

Use the position function …

01:04

02:31

Given the following accele…

02:09

Acceleration to position G…

02:03

02:07

Find the position function…

01:58

Give the acceleration $a=d…

01:13

Velocity and acceleration …

in this exercise were given the position of an object as a function of time here in the screen on the screen. And Maria asked to find What is the acceleration vector relate into this trajectory? So let's first find what the velocity is. Let's find the velocity vector. Let's remind ourselves that the velocity vector is the derivative off the position with respect two time so V. It was the derivative of our with respect to time. Ah, so let's do it Well, the first term is 3.2 t The derivative off tea with respect to T is one. So we only get to to the second term is 1.8 t square derivative of T Square is to t. So we're gonna have to times 1.8 times t that is the 0.60. Okay, I and then the same thing for the the why component. It's 1.7 minus 4.8 again, we're just deriving only know Mia's here. Well, you know, meals here j And then finally Ah, the exploration aid. The acceleration vector is the derivative off the velocity with respect to time. So it's the V ditty. Uh for the first time term. The derivative off a constant is zero. So it's simply gonna ah, disappear. The derivative of tea is one. So Ah, for the second term, we're gonna have 3.6 i in the same thing for the second term. The first, the 1.1 point seven is gonna simply vanish. And the riveter of 4.8 times T is 4.8. Eso have for minus 418 Jay. So the final acceleration is through in six I, minus four point A J meters per second squared, and this is our final answer.

View More Answers From This Book

Find Another Textbook

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 position of an object as a function of time is given by $\vec{r}=\left(3…

Find the velocity and acceleration functions for the given position function…

Use the position function $f(t)$ meters to find the velocity at time $t=a$ s…

Given the following acceleration functions of an object moving along a line,…

Acceleration to position Given the following acceleration functions of an ob…

Find the position function from the given velocity or acceleration function.…

Give the acceleration $a=d^{2} s / d t^{2},$ initial velocity, and initial p…

Velocity and acceleration from position Consider the following position func…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.