The displacement of a particle is given by \(y = a + bt + ct^{2} - dt^{4}\). The initial velocity and acceleration are, respectively:

1. \(b, -4d\) 2. \(-b,2c\)
3. \(b, ~2c\) 4. \(2c, -2d\)
Subtopic:  Non Uniform Acceleration |
 83%
Level 1: 80%+
PMT - 1999
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A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to \(v(x)= βx^{- 2 n}\) where \(\beta\) and \(n\) are constants and \(x\) is the position of the particle. The acceleration of the particle as a function of \(x\) is given by:
1. \(- 2 nβ^{2} x^{- 2 n - 1}\) 2. \(- 2 nβ^{2} x^{- 4 n - 1}\)
3. \(- 2 \beta^{2} x^{- 2 n + 1}\) 4. \(- 2 nβ^{2} x^{- 4 n + 1}\)
Subtopic:  Non Uniform Acceleration |
 70%
Level 2: 60%+
NEET - 2015
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The acceleration of a particle starting from rest varies with time according to the relation \(A= - a\omega^2\sin \omega t\). The displacement of this particle at a time \(t\) will be:
1. \(-\frac{1}{2}\left(a\omega^2\sin\omega t\right)t^2\) 2. \(a\omega \sin \omega t\)
3. \(a\omega \cos \omega t\) 4. \(a\sin \omega t\)
Subtopic:  Non Uniform Acceleration |
 62%
Level 2: 60%+
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A particle is moving along the \(x\)-axis such that its velocity varies with time as per the equation \(v = 20\left(1-\frac{t}{2}\right) \). At \(t=0 \) particle is at the origin. From the following, select the correct position \((x)\) - time \((t)\) plot for the particle:

1.   2.
3. 4.

 
Subtopic:  Non Uniform Acceleration |
 61%
Level 2: 60%+
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