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