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Motion in A Straight Line question

2005 · Q154
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Motion in A Straight Line question

2005 · Q154

NEETPhysicsMotion in A Straight LineMCQ+4 / −1
The displacement x of a particle varies with time t as x = ae−-−at + beβ\betaβt, where a, b, α\alphaα and β\betaβ are positive constants. The velocity of the particle will
  1. A
    be independent of β\betaβ
  2. B
    drop to zero when α\alphaα = β\betaβ
  3. C
    go on decreasing with time
  4. D
    go on increasing with time.
View written solutionFree

Correct answer: D

x = ae-$$\alpha t + beβ\beta βt

dxdt{{dx} \over {dt}}dtdx​ = - α\alpha αae-$$\alpha t + bβ\beta βeβ\beta βt

v = - α\alpha αae-$$\alpha t + bβ\beta βeβ\beta βt

Velocity will go on increasing with time.

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