Phy-motion
2011-07-25 2:54 am
A particleis moving along a straight line. At time t, the velocity of the particle is v.The acceleration of the particle throughout the motion is –[λ/(v^1/4)], whereλis a positive constant. The velocity of the particle is u when t=0. Find v in terms of u, λ and t
回答 (1)
2011-07-25 6:01 am
✔ 最佳答案
Given acceleration a = –[λ/(v^1/4)]but by definition, a = dv/dt
hence, dv/dt = –[λ/(v^1/4)]
(v^1/4)dv = (-λ)dt
integrate on both sides,
(4/5)v^(5/4) = -λt + C, where C is the integration constant
Since at t = 0, v = u
hence, (4/5)u^(5/4) = C
Therefore, (4/5)v^(5/4) = (4/5)u^(5/4) -λt
v^(5/4) = u^(5/4) - (5/4)λt
i.e. v = [ u^(5/4) - (5/4)λt]^(4/5)
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