Two cars \(\mathrm{P}\) and \(\mathrm{Q}\) 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 |
 80%
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. \(24\) m 2. \(40\) m
3. \(56\) m 4. \(16\) 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 |
 52%
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. \(0\)
4. none of the above

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 81%
From NCERT
AIPMT - 1999
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