Question

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 3 sin πt + 5 cos πt, where t is measured in seconds. (Round your answers to two decimal places.)
(a) Find the average velocity during each time period.
[1,2]
[1,1.1]
[1,1.01]
[1,1.001]
(b) Estimate the instantaneous velocity of the particle when t = 1.

Answer 1

Differentiate.

Answer 2

i'm sorry what do you mean?

Answer 3

ds / dt
similar to dy/dx ~does that look familiar?

Answer 4

not at all... if you could explain it and help me work through the problems that would be helpful.

Answer 5

what math are you in

Answer 6

calc

Answer 7

Ok, what is the title of the chapter you're on?

Answer 8

Differentiation, so you should read it

Answer 9

2.1 is the chapter

Answer 10

also you should memorize trig identities
(d/dx)(sin(x)) = cos(x)
(d/dx)(cos(x)) = -sin(x)

Answer 11

okay I'm opening my textbook up now to take another look

Answer 12

the chain rule is also very important:
http://www.eeweb.com/pics/math/calc_deriv/derivative_chain_rule_sin.gif

http://0.tqn.com/y/math/1/S/5/O/chain_rule.gif

Answer 13

d/dx of position (displacement) = velocity
d/dx of velocity = acceleration
d/dx of acceleration = jerk
etc...
snap
crackle
pop
jouce

Answer 14

okay

Answer 15

I'm looking at my textbook and it still is making no sense

Answer 16

lol

Answer 17

this guy is the best:
https://www.youtube.com/watch?v=pFeuGMMiZWw

Answer 18

she's also pretty good:
https://www.youtube.com/watch?v=4GaxepQ2j-s