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Particle Motion - Unit 2
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Terms in this set (18)
Take the derivative; v(t) = x'(t)
Given x(t), find v(t)
Take the second derivative; a(t) = x"(t)
Given x(t), find a(t)
--Method--
(1) Find all t's where x'(t) = 0
(2) Find x(t) for all t's from Step 1 AND endpoints
(3) Find the distance traveled over each interval
(4) Find the sum of the abs. value of all distances from Step 3
Given x(t), find total distance traveled on [a,b]
x(b) - x(a)
Given x(t), find the displacement on [a,b]
When v(t) and a(t) have the same signs.
When is the particle speeding up?
When v(t) and a(t) have opposite signs.
When is the particle slowing down?
When v(t) > 0
When is the particle moving right?
When v(t) < 0
When is the particle moving left?
When v(t) = 0
When is the particle at rest?
[x(b) - x(a)] / [b - a]
Given x(t), find the average velocity on [a,b].
[v(b) - v(a)] / [b - a]
Given v(t), find the average acceleration on [a,b].
When v(t) changes signs.
--Method--
(1) Look for where v(t) = 0 or is undefined.
(2) Create a sign chart to find where v(t) changes signs
When does the particle change direction?
Take the derivative; instantaneous velocity = v(t) = x'(t)
Given x(t), find the instantaneous velocity.
set numerator of f'(x) = 0
Find horizontal tangent lines of f(x)
set denominator of f'(x) = 0
Find vertical tangent lines of f(x)
v(t) = [x(b) - x(a)] / [b-a]
Find when the instantaneous velocity is the same as the average velocity.
y-f(a) = f'(a)(x-a)
Equation of a line tangent to f(x) at x=a
|v(t)|
Speed
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