Respuesta :
Explanation:
Given that,
The vertical motion of mass A is defined by the relation as :
[tex]x=10\ sin2t+15\ cos2t+100[/tex]
At t = 1 s
[tex]x=10\ sin2+15\ cos2+100[/tex]
x = 115.33 mm
(a) We know that,
Velocity, [tex]v=\dfrac{dx}{dt}[/tex]
[tex]v=\dfrac{d(10\ sin2t+15\ cos2t+100)}{dt}[/tex]
[tex]v=20\ cos2t-30\ sin2t[/tex]
At t = 1 s
[tex]v=20\ cos2-30\ sin2[/tex]
v = 18.94 mm/s
We know that,
Acceleration, [tex]a=\dfrac{dv}{dt}[/tex]
[tex]a=\dfrac{d(20\ cos2-30\ sin2)}{dt}[/tex]
[tex]a=-40\ cos2t-60\ cos2t[/tex]
At t = 1 s
[tex]v=-40\ cos2-60\ cos2[/tex]
[tex]a=-99.93\ mm/s^2[/tex]
(b) For maximum velocity, [tex]\dfrac{dv}{dt}=a=0[/tex]
[tex]-40\ cos2t-60\ cos2t=0[/tex]
t = 45 seconds
For maximum acceleration, [tex]\dfrac{da}{dt}=0[/tex]
[tex]80\ sin2t+120\ cos2t=0[/tex]
t = 61.8 seconds
Hence, this is the required solution.
