Given the position function of a particle in motion how do you find (1) velocity at time t and at a specific time

Velocity equation is first derivative of position equation. Plug in a specific number for the variable.

Given the position function of a particle in motion how do you determine (2) when the particle is at rest

You plug 0 into the velocity equation. There might be more than one answer.

Given the position function of a particle in motion how do you find (3) whether the movement is pos or neg

plug in different numbers between the numbers where it's at rest and see if it's positive or negative. Negative velocity denotes that it's moving backward, positive velocity means moving forward

Given the position function of a particle in motion how do you determine (4) total distance traveled in set amount of time

You plug in v(o) and then the values of v(t) that you got earlier and then v( whatever the set amount of time is). That gives you distances, then you find distances between intervals. Then you add all of those up.

Given the position function of a particle in motion how do you find (5) acceleration at time t

the derivative of the velocity equation is the acceleration equation. set it equal to 0 to find multiple times where the particle is stopped. plug that into the equation to find a.

Given the position function of a particle in motion how do you determine (6) if the particle is speeding up or slowing down

if velocity and acceleration have the same sign, it's speeding up. If they're working against each other, it's slowing down.

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Calc 2.7

Chapter 2.7 of calculus, major concepts for review

Question	Answer
What are rates of change?	If a function represents position over time, then its derivative represents the rate of change in position with respect to time or velocity
What is the particle in motion problem?	Given the position function find (1) velocity at time t and at a specific time (2) when the particle is at rest (3) whether the movement is pos or neg (4) total distance traveled in set amount of time (5) acceleration at time t, (6) speeding up or slowing
Given the position function of a particle in motion how do you find (1) velocity at time t and at a specific time	Velocity equation is first derivative of position equation. Plug in a specific number for the variable.
Given the position function of a particle in motion how do you determine (2) when the particle is at rest	You plug 0 into the velocity equation. There might be more than one answer.
Given the position function of a particle in motion how do you find (3) whether the movement is pos or neg	plug in different numbers between the numbers where it's at rest and see if it's positive or negative. Negative velocity denotes that it's moving backward, positive velocity means moving forward
Given the position function of a particle in motion how do you determine (4) total distance traveled in set amount of time	You plug in v(o) and then the values of v(t) that you got earlier and then v( whatever the set amount of time is). That gives you distances, then you find distances between intervals. Then you add all of those up.
Given the position function of a particle in motion how do you find (5) acceleration at time t	the derivative of the velocity equation is the acceleration equation. set it equal to 0 to find multiple times where the particle is stopped. plug that into the equation to find a.
Given the position function of a particle in motion how do you determine (6) if the particle is speeding up or slowing down	if velocity and acceleration have the same sign, it's speeding up. If they're working against each other, it's slowing down.

Created by: haleyBUGoxox

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