A particle is moving along the \(x\text-\)axis with its position \((x)\) varying with time \((t)\) as \(x=\alpha t^{4}+\beta t^{2}+\gamma t+\delta.\) The ratio of its initial velocity to its initial acceleration is:
1. \(2\alpha:\delta \)
2. \(\gamma:2\delta \)
3. \(4\alpha:\beta \)
4. \(\gamma:2\beta \)
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 80%
From NCERT
NEET - 2024
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Two cars \(P\) and \(Q\) start from a point at the same time in a straight line and their positions are represented by; \(x_p(t)= at+bt^2\) and \(x_Q(t) = ft-t^2. \) At what time do the cars have the same velocity?
1. \(\frac{a-f}{1+b}\)

2. \(\frac{a+f}{2(b-1)}\)

3. \(\frac{a+f}{2(b+1)}\)

4. \(\frac{f-a}{2(1+b)}\)

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 81%
From NCERT
NEET - 2016
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If the velocity of a particle is \(v=At+Bt^{2},\) where \(A\) and \(B\) are constants, then the distance travelled by it between \(1~\text{s}\) and \(2~\text{s}\) is:

1. \(3A+7B\) 2. \(\frac{3}{2}A+\frac{7}{3}B\)
3. \(\frac{A}{2}+\frac{B}{3}\) 4. \(\frac{3A}{2}+4B\)
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 88%
From NCERT
NEET - 2016
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A particle moves along a straight line \(OX.\) At a time \(t\) (in seconds), the displacement \(x\) (in metres) of the particle from \(O\) is given by \(x= 40 +12t-t^3.\) How long would the particle travel before coming to rest?
1. \(24~\text m\) 2. \(40~\text m\)
3. \(56~\text m\) 4. \(16~\text m\)
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
From NCERT
AIPMT - 2006
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The displacement \(x\) of a particle varies with time \(t\) as \(x = ae^{-\alpha t}+ be^{\beta t}\), where \(a,\) \(b,\) \(\alpha,\) and \(\beta\) are positive constants. The velocity of the particle will:

1. be independent of \(\alpha\) and \(\beta.\)
2. go on increasing with time.
3. drop to zero when \(\alpha=\beta.\)
4. go on decreasing with time.
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 53%
From NCERT
AIPMT - 2005
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For a particle, displacement time relation is given by; t = x + 3 . Its displacement, when its velocity is zero will be:
1. \(2\) m
2. \(4\) m
3. \(0\) m
4. none of the above

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 82%
From NCERT
AIPMT - 1999
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