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 – t3. 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 $$x = ae^{-\alpha t}+ be^{\beta t}$$$\mathrm{}$
, 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 $t$ $=$ $\sqrt{x}$ $+$ $3$ . 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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