A street car moves rectilinearly from station A to the next station B with an acceleration varying according to the law f = a − b x , where a and b are positive constants and x is the distance from st

Question

A street car moves rectilinearly from station A to the next station B with an acceleration varying according to the law f = a − b x , where a and b are positive constants and x is the distance from station A . The distance between the two stations and the maximum velocity are:

TestHub · Accepted Answer

v d x d v ​ = a − b x integrates to 2 v 2 ​ = a x − 2 b x 2 ​ . The car stops again at x = b 2 a ​ ; v is maximum where f = 0 , i.e. x = b a ​ , giving v ma x 2 ​ = 2 ( b a 2 ​ − 2 b a 2 ​ ) = b a 2 ​ , so v ma x ​ = b ​ a ​ . Option A.

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Options:

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