3.4 to 3.5 particle motion and trig functions
csc^2x-cot^2x
1 (csc and cot)
sin^2x+cos^2x
1 (pythagorean identity)
sec^2x-tan^2x
1 (sec and tan)
you take the position it gained going right and subtract it to the position it gained going left
How do you find displacement when givin a graph
If you have two different signs - Positve slope in the negative part of the graph - negative slope in the positive of the graph
How do you know if a particle is slowing down
Negative slope on negative part of the graph, positive slope on the positive part of the graph
How do you know if a particle is speeding up?
You want to find when the velocity is o first by finding the derivative of the speed equation, then setting it = to 0. Then, once that is done, you want to plug those numbers into the acceleration equation, which is the derivate of the velocity equation
How would you solve this: The position of a body at time t sec is s(t) = 6t^2 + 9t m. Find the body's acceleration each time the velocity is zero?
put 100 into the original equation, then then divide by how many wahsing machines you are solving for to find the unit cost basically
If the question is asking you to find average cost of producing 100 washing machines with an equation c(x) = 2000 + 100x - 0.1x^2 , how do you solve for it?
You find the derivative of the equation, then you plug in 100
If the question is asking you to find the marginal cost when 100 machines are produced with an equation c(x) = 2000 + 100x - 0.1x^2 , how do you solve for it?
You graph it as an absolute value function
If you are given a speed graph, and then are asked to graph velocity, how do you do it?
A particle changes direction when a velocity is 0, so you want to set the velocity equation = to 0 and then solve for t
If you have the equation s(t) = t^2 - 3t +2, and the question asks: ) At what values of t does the particle change direction?, how do you solve it?
Find the acceloration, which is the derivative of the velcoity. When you do that, the answer is just two. So at any time the acceloration will be 2m/s^2
If you have the equation s(t) = t^2 - 3t +2, and the question asks: ) Find the acceleration of the particle when t = 4, how do you solve it?
Velocity is the slope of the speed, so you find the slop from 5 to 0, by pluging in five and 0 and then use slope equation
If you have the equation s(t) = t^2 - 3t +2, and the question asks: Find the average velocity during the first 5 seconds, how do you solve it
plug 5 in for t, plug 0 in for t (bc 0 is staring position) and then subtract the two
If you have the equation s(t) = t^2 - 3t +2, and the question asks: Find the displacement during the first 5 seconds, how do you solve it
You want to find the velocity funciton of the position one (which is the derivative), then plug in 4
If you have the equation s(t) = t^2 - 3t +2, and the question asks: Find the instantaneous velocity when t = 4, how do you solve it?
s(t) is at its minimum when velocity is 0, so we take the zero of velocity (which we found from last equation) and plug it into the speed equation to get the position
If you have the equation s(t) = t^2 - 3t +2, and the question asks: Where is the particle when s is a minimum, how do you solve it?
you want to set the position = to 0 and solve for t
If you want to see how long something was in the air, hwo do you calculate it?
put 100 into original equation, then 101 into the equation and subtract the two
Show that the marginal cost when 100 washing machines are produced is approximately the cost of producing one more washing machine after the first 100 have been made, by calculating the latter cost directly. When the equation is c(x) = 2000 + 100x - 0.1x^2. How do you solve this?
That is when the particle is changing direction
When a velocity graph crosses the x axis, what does the point on the x axis mean? What does the zero mean?
acceloration
derivative of velocity
Marginal costs
fist derivative of the cost function with respect to the level of production
You use the displacement, then subtract out the given starting position
how do you find the particles finishing position
graph slope at each interval
how do you graph acceloration on a velocity graph
displacement
how far it went
positive
if the graph of speed is increasing than the acceloration is
going to the right or up
if the graph of speed is increasing than the position is
positive and velocity/slope is increasing
if the graph of speed is increasing than the velocity is
zero
if the slope of a velocity graph is constant, then acceloration is
acceleration is negative
if velocity is negative and decreasing, then acceloration is
second derivative
if velocity is the derivative of speed, then acceloration is the _______ of speed
postion function
s(t) is the
absolute value
speed is the _______ of velocity
m/s^2
unit for acceleration if speed is m and velocity is m/s
Since speed is absolute value of velcosity, you take points on the graph where velocity is at its highest and lowst and that is the greates speed
what is a particle travelling at its greatest speed?
Marginal reveue is the same thing but with income
what is marginal revenue compared to marginal cost
-sinx
what is the derivative of cosx
-csc^2x
what is the derivative of cotx
-cscxcotx
what is the derivative of cscx
secxtanx
what is the derivative of secx
cosx
what is the derivative of sinx
velocity
what is the derivative of speed
sec^2x
what is the derivative of tanx
when the velocity is 0
when is a particle at rest?
when the graph is negative
when is the particle moving to the left
when the graph of velocity shows it as a negaitve
when is the particle moving to the left
when the graph is positive
when is the particle moving to the right
You have to use the product rule
when you take the second derivative of csc or sec, how do you do it?