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# Math III

### Particle Motion & Related Rates

How to find position formula should be given to you; x(t)
Find velocity at time t. Find velocity formula; find derivative of x(t)
When is the particle at rest? set v(t)=0; solve for t
When is the particle moving in a positive direction? set v(t)>0; use zeros on ↔ to find when values are +
Find acceleration at time t. Find derivative of v(t) or find x''(t)
initial velocity of the particle find v(0)
Is the particle accel. or decel. at t=__ sec? Find accel. of whatever time given; determine by > or <
Accelerating or decelerating ? a(3)>0 accelerating
Accelerating or decelerating? a(3)<0 decelerating
In what direction is the particle moving at t=__sec? Find v of whatever time is given; determine by > or <
In what direction is the particle moving if v is +? ↑ or →
In what direction is the particle moving if v is -? ↓ or ←
When is the particle slowing down? when a(t) & v(t) have opposite signs on ↔
when given dy/dx which variable will have a derivative w/o needing the notation? x
What is the unit for volume using ft? ft^3
What is the unit for area using ft? ft^2
What is the unit for anything else using ft? ft
What does "how fast" mean for a related rates problem? find the rate
When doing any related rates problem what will always be at the bottom (i.g. dy/dx)? dt
When doing any related rates problem what will always be at the top (i.g. dy/dx)? whatever you're looking for
*don't forget to study/practice graph & chart problems!* N/A
When is the particle speeding up? when a(t) & v(t) have the same sign on ↔
Give all the times when the object is moving → set v(t)>0; use zeros on ↔ to find when values are +
another way to ask when is the particle moving in a positive direction Give all the times when the object is moving →
Find the times when the particle changes direction Give intervals where v(t) & a(t) have the same sign w/o including - numbers
When writing time intervals what type of numbers should you NEVER include? negative numbers
Why should you never include negative numbers when talking about time? time is never negative
area of square formula A=s^2
area of circle formula A=pi*r^2
volume of cube formula V=s^3
Created by: OnChromebook