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A particle moves to two dimensional orbit defined by x(t) =A(2at-sinat) y(t)=A(1-cosat) A) Find the tangential acceleration a1 and normal acceleration an as function of time where the tangential and normal components are taken with respect to the velocity. B) Determine at what times in the orbit an has a maximum.

A particle moves to two dimensional orbit defined by x(t) =A(2at-sinat) y(t)=A(1-cosat) A) Find the tangential acceleration a1 and normal acceleration an as function of time where the tangential and normal components are taken with respect to the velocity. B) Determine at what times in the orbit an has a maximum.

Grade:6

1 Answers

Vikas TU
14149 Points
5 years ago
(1)  Tangential acceleration a1 = dv/dt = d^2x(t)/dt^2 
dx/dt = A(2a –acos(at))
dv/dt = A(a^2sin(at))
a1 = A(a^2sin(at))
 
Normal acceleration would be: d^2y(t)/dt^2 
dy/dt = Aasin(at)
d^2y/dt^2 = Aa^2cos(at) 
an = Aa^2cos(at) 
 
(2) For an to be maximum, d(an)/dt = 0
Aa^3sin(at) = 0
at = npi
t = n*pi/a it will be maximum. 

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