A particle moves along the x-axis so that its velocity at any time t≥0 is given by the function..?
A particle moves along the x-axis so that its velocity at any time t≥0 is given by the function v(t)=(2(pi)-5)t-sin((pi)t).
A. Find the acceleration at any time t.
B. Find the minimum acceleration of the particle over the interval [0,3].
C. Find the maximum velocity of the particle over the interval [0,2].
Please show work.
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v(t) = (2π−5)t − sin(πt) m/s
A. a(t) = dv/dt = (2π−5) −πcos(πt)
B. a(0) = (2π−5) - πcos0 = π−5 m/s²
a(3) = (2π−5) - πcos3π = (2π−5) + π = 3π−5 m/s²
Minimum value of a(t) = π−5 m/s² at t = 0 sec (also at t = 2 sec)
C. v(0) = 0 m/s,
v(2) = 2(2π−5) m/s = (4π−10) m/s
v_max = v(2) = (4π−10) m/s
Hope that helped.
Now, 10 pts pleeeez.