A street car moves rectilinearly from station A (here car stops) to the next station B (here also car stops) with an acceleration varying according to the law f = a - bx, where a and b are positive constants and x is the distance from station A. If the maximum distance between the two stations is x = 
then find N
Text Solution
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(2)
f = a – bx
For maximum velocity, acceleration should be zero.
i.e. a – bx = 0
⇒ x = 
∴ At x = 
, the particle has its maximum velocity.
f = 
= a – bx
⇒ 
= 
At x = 0 ; v = 0
⇒ c = 0
Substituting; x = 
; gives
v max = 
Also, the velocity of the car should become zero at station B.
i.e. 
⇒ x = 0 ; x = 
∴ Distance between the two stations is 
∴ N = 2
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