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A particle starts from point A moves along a straight line path with an acceleration 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 particle is
  • a)
    p/q
  • b)
    p/√q
  • c)
    q/p
  • d)
    √q/p
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A particle starts from point A moves along a straight line path with a...
Given: a = p − qx
At maximum velocity, a = 0
⇒ 0 = p - qx or x = p/q
∴  Velocity is maximum at  x = p/q
since Acceleration 


vdv = (p − qx)dx 
Integrating both sides of the above equation, we get
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Most Upvoted Answer
A particle starts from point A moves along a straight line path with a...
To fully answer this question, we need additional information about the acceleration function. The given acceleration is written as "a = p," but we need to know the value of p in order to determine the motion of the particle.

If we have the value of p, we can integrate the acceleration function to find the velocity function and then integrate the velocity function to find the position function.

First, let's integrate the acceleration function:
∫ a dt = ∫ p dt
v = pt + C1

Next, we integrate the velocity function to find the position function:
∫ v dt = ∫ (pt + C1) dt
s = (1/2)pt^2 + C1t + C2

Here, C1 and C2 are constants of integration.

Without the value of p, we cannot determine the specific equations for velocity and position.
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