# The position of a particle with respect to time $$t$$ along the $$\mathrm{x}$$-axis is given by $$9t^{2}-t^{3}$$ where x is in metre and $$t$$ in second. What will be the position of this particle when it achieves maximum speed along the $$+\mathrm{x}$$ direction? 1. $$32$$ m 2. $$54$$ m 3. $$81$$ m 4. $$24$$ m

Subtopic:  Non Uniform Acceleration |
77%
From NCERT
AIPMT - 2007
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A car moves from $$X$$ to $$Y$$ with a uniform speed $$v_u$$ and returns to $$X$$ with a uniform speed $$v_d.$$ The average speed for this round trip is:

 1 $$\frac{2 v_{d} v_{u}}{v_{d} + v_{u}}$$ 2 $$\sqrt{v_{u} v_{d}}$$ 3 $$\frac{v_{d} v_{u}}{v_{d} + v_{u}}$$ 4 $$\frac{v_{u} + v_{d}}{2}$$
Subtopic:  Average Speed & Average Velocity |
82%
From NCERT
AIPMT - 2007
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A particle moving along the x-axis has acceleration $$f,$$ at time $$t,$$ given by, $$f=f_0\left ( 1-\frac{t}{T} \right ),$$  where $$f_0$$ and $$T$$ are constants. The particle at $$t=0$$ has zero velocity. In the time interval between $$t=0$$ and the instant when $$f=0,$$ the particle’s velocity $$\left ( v_x \right )$$ is:
1. $$f_0T$$
2. $$\frac{1}{2}f_0T^{2}$$
3. $$f_0T^2$$
4. $$\frac{1}{2}f_0T$$

Subtopic:  Non Uniform Acceleration |
57%
From NCERT
AIPMT - 2007
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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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Two bodies, $$A$$ (of mass $$1~\text{kg}$$) and $$B$$ (of mass $$3~\text{kg}$$) are dropped from heights of $$16~\text{m}$$ and $$25~\text{m}$$, respectively. The ratio of the time taken by them to reach the ground is:
1. $$\frac{5}{4}$$
2. $$\frac{12}{5}$$
3. $$\frac{5}{12}$$
4. $$\frac{4}{5}$$

Subtopic:  Uniformly Accelerated Motion |
80%
From NCERT
AIPMT - 2006
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A particle moves in a straight line with a constant acceleration. It changes its velocity from $$10$$ ms-1 to $$20$$ ms-1 while covering a distance of $$135$$ m in $$t$$ seconds. The value of $$t$$ is:

 1 $$10$$ 2 $$1.8$$ 3 $$12$$ 4 $$9$$
Subtopic:  Uniformly Accelerated Motion |
79%
From NCERT
AIPMT - 2008
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A particle shows the distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point:

1. B
2. C
3. D
4. A

Subtopic:  Graphs |
79%
From NCERT
AIPMT - 2008
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The distance travelled by a particle starting from rest and moving with an acceleration $$\frac{4}{3}$$ ms-2, in the third second is:
1. $$6$$ m
2. $$4$$ m
3. $$\frac{10}{3}$$ m
4. $$\frac{19}{3}$$ m

Subtopic:  Distance & Displacement |
79%
From NCERT
AIPMT - 2008
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A particle starts its motion from rest under the action of a constant force. If the distance covered in the first $$10$$ s is $$S_1$$ and that covered in the first $$20$$ s is $$S_2$$, then:
1. $$S_2=2S_1$$
2. $$S_2 = 3S_1$$
3. $$S_2 = 4S_1$$
4. $$S_2= S_1$$

Subtopic:  Acceleration |
70%
From NCERT
AIPMT - 2009
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A bus is moving at a speed of $$10$$ ms-1 on a straight road. A scooterist wishes to overtake the bus in $$100$$ s. If the bus is at a distance of $$1$$ km from the scooterist, with what speed should the scooterist chase the bus?
1. $$20$$ ms-1
2. $$40$$ ms-1
3. $$25$$ ms-1
4. $$10$$ ms-1
Subtopic:  Relative Motion in One Dimension |
77%
From NCERT
AIPMT - 2009
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