The velocity of a particle moving along the x axis is given by vx = a t − b t3 for t > 0 , where a = 29 m/s2,?
The velocity of a particle moving along the x
axis is given by
vx = a t − b t3 for t > 0 ,
where a = 29 m/s2, b = 2.5 m/s4, and t is in
s.
What is the acceleration ax of the particle
when it achieves its maximum displacement
in the positive x direction? Answer in units
of m/s2.
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Verified answer
The displacement of the particle is x = ∫v*dt; we find the maximum displacement from setting dx/dt = 0. However dx/dt = v. so max displacement occurs when v = 0
a*tm - b*tm³ = 0;
a - b*tm² = 0
tm= ±√[a/b]
tm = ±3.4
a = 29 - 3*2.5*3.4² = 58 m/s (same for tm = -3.4)
Integrating to get x, x = ½*a*t² - ¼*b*t^2
x(3.4) = 84
x(-3.4) = 84
both positive