Question

A particle moves along the $x$ axis according to the equation $x=2.00+3.00 t-t^{2}$, where $x$ is in meters and $t$ is in seconds. At $t=3.00 \mathrm{~s}$, find (a) the position of the particle, (b) its velocity, and (c) its acceleration.

Name: Problem 17, Chapter 2: Fundamentals of Physics
Uploaded: 2021-06-16T10:43:32-08:00
Duration: 2 min 6 s
Channel: Prabhu Ramji
Description: A particle moves along the x axis according to the equation x=2.00+3.00 t-t^2, where x is in meters and t is in seconds. At t=3.00 s, find (a) the position of the particle, (b) its velocity, and (c) its acceleration.

   A particle moves along the $x$ axis according to the equation $x=2.00+3.00 t-t^{2}$, where $x$ is in meters and $t$ is in seconds. At $t=3.00 \mathrm{~s}$, find (a) the position of the particle, (b) its velocity, and (c) its acceleration.

Fundamentals of Physics

David Halliday,… 8th Edition

Chapter 2, Problem 17

Instant Answer

Solved by Expert Prabhu Ramji

06/16/2021

Step 1

00+3.00 t-t^{2}$. We need to find the position at $t=3.00 \mathrm{~s}$. We substitute $t=3.00$ into the equation to find the position. Show more…

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A particle moves along the $x$ axis according to the equation $x=2.00+3.00 t-t^{2}$, where $x$ is in meters and $t$ is in seconds. At $t=3.00 \mathrm{~s}$, find (a) the position of the particle, (b) its velocity, and (c) its acceleration.

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Key Concepts

Position Function

A position function describes the location of a particle along a coordinate axis as a function of time. It encapsulates the motion of the particle by providing its coordinate value at every instant, helping us understand its path and overall displacement in one-dimensional motion.

Instantaneous Velocity

Instantaneous velocity is defined as the rate of change of the position function with respect to time. It is obtained by differentiating the position function, capturing both the speed and the direction of the motion at any given instant.

Instantaneous Acceleration

Instantaneous acceleration represents the rate at which the velocity changes over time. This quantity is found by differentiating the velocity function (or equivalently taking the second derivative of the position function) and indicates how quickly the particle’s motion is speeding up or slowing down.

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