Q.

A particle starts from point A moves along a straight line path with an aceleration given by a = p - qx where p,q are constants and x is distance from point A. The particle stops at point B. The maximum velocity of the paticle is

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a

b

c

d

answer is B.

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Detailed Solution

Acceleration a = (p - qx)The velocity is maximum when dv/dx = 0Now,   velocity is zero when a = p - qx = 0 i.e. x = p/qNow, v. dv = (p - qx)dx⇒∫0xmv dv =p∫0pq dv -q∫0pqxdx    ⇒vm=pq
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A particle starts from point A moves along a straight line path with an aceleration given by a = p - qx where p,q are constants and x is distance from point A. The particle stops at point B. The maximum velocity of the paticle is