Velocity, Acceleration and Distance


by clipperdude21
Tags: acceleration, distance, velocity
clipperdude21
clipperdude21 is offline
#1
Nov1-07, 02:21 PM
P: 49
1.11. If position of an object is given by: x(t) = A sin(ωt) where A is a constant and ω is
the angular frequency.
a) What is the instantaneous velocity at time t?
b) What is the instantaneous acceleration at time t?
c) Express the instantaneous velocity and the instantaneous acceleration in terms of
x, ω and A.




2. dx(t)/dt= v(t)
dv(t)/dt=a(t)




3. a) For (a) I just took the derivative of the x function and got wAcos(wt)
b) Same thing here but took the derivative for the answer i got in A and got
-w^2Asin(wt)
c) This is where i had some trouble. I got the instantaneous acceleration part of the
problem by substituting x for Asin(wt) and thus got a(t)=-w^2x. But i had no
clue how to get v(t) in terms of x,w,A.

What i did was set sin^2(wt) + cos^2(wt)=1 and solved for cos^2(wt). then plugged that into v^2(t)=w^2A^2cos^2(wt). I got v^2=w^2(A^2-x^2). After taking the square root i got v = +/-(w * sqrt(A^2-x^2). Is this right? should there be the +/- or is one ruled out?


Thanks for the help in advance!\sqrt{}
Phys.Org News Partner Science news on Phys.org
Review: With Galaxy S5, Samsung proves less can be more
Making graphene in your kitchen
Study casts doubt on climate benefit of biofuels from corn residue
Dick
Dick is offline
#2
Nov1-07, 03:34 PM
Sci Advisor
HW Helper
Thanks
P: 25,171
Good job! No, you can't pick one of the +/-. You need them both. At a given value of x, v can be either negative or positive depending on whether x is increasing or decreasing. And it could be doing either.


Register to reply

Related Discussions
Acceleration when velocity is a function of distance Introductory Physics Homework 7
finding velocity with changing distance and acceleration Introductory Physics Homework 4
Acceleration, velocity, distance, speed and time help please Astrophysics 4
problem (acceleration/velocity/distance) Introductory Physics Homework 1
questions on kinematics (distance/velocity/acceleration) Introductory Physics Homework 9