Physics problem to solve

label Physics
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The position of a particle is given by the expression x = 4.00 cos(3.00πt + π), where x is in meters and t is in seconds. Determine (a) the frequency and (b) period of the motion, and (e) the position of the particle at t = 0.250 s, (e) the speed of the particle at t = 0.250 s, and (e) the acceleration of the particle at t = 0.250 s.

Nov 17th, 2015

Thank you for the opportunity to help you with your question!

a) frequency,f = w/2pi = 3.00pi/[2*pi] = 1.5 Hz

b) period of motion , T =2*pi/w = 2*pi/[3*pi] = 0.666 s

c)the position of the particle at t = 0.250 s,

x = 4cos[3pi*0.25+pi] = 2.828 m

d)the speed of the particle at t = 0.250 s,

v=dx/dt = -12pi*sin[3pit+pi] at t=0.25

v = -12pi*sin[3pi/4 + pi] = 26.657 m/s

e)the acceleration of the particle at t = 0.250 s,

a = dv/dt = -36pi*cos[3pi*t+pi]

    = -36pi^2*cos[3pi/4 +pi] = 251.239 m^2/s


Please let me know if you need any clarification. I'm always happy to answer your questions.
Nov 17th, 2015

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