# Velocity/displacement problem

• Sep 29th 2009, 04:28 PM
sub0
Velocity/displacement problem
Hello,

I am not very good at calculus to begin with, especially word problems and velocity problems. I have no idea how to start this one out, so if someone could show me how, that would be great to give me a start. Here goes:

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 5sin(πt) + 2cos(πt), where t is measured in seconds. (Round all answers to the nearest hundredth.)

there are multiple sub-questions, but I'll just give two:

(a) Find the average velocity during the time period [1, 2] (in cm/s).
(e) Estimate the instantaneous velocity of the particle when t = 1 (in cm/s).

I haven't the slightest clue other than I'm (guessing) it has something to do with Galileo's law, s(t) = 4.9t^2,but I have no clue where/when I should apply it or in addition to another formula.

Any help would be awesome! Thanks. :)
• Sep 29th 2009, 04:59 PM
Calculus26
No this has nothing to do with Galileo's Law it is a completely different
motion problem.

What stays the same is the definition of average velocity it is still

[s(t2) - s(t1)]/(t2-t1)

s = 5sin(πt) + 2cos(πt

Compute [s(2) -s(1)]/[2-1]

The instantaneous velocity is the derivative but as you've been asked for
an approximation I'm assuming you haven't done derivatives yet?

Compute [s(1.01) -s(1)]/[1.01-1]
• Sep 29th 2009, 05:20 PM
sub0
No, we haven't done derivatives yet, those are in the next unit. I was just thinking it may have something to do with Galileo's Law because the question previous had it and the beginning of the section explains it. I will give it a try, thanks for the help :)