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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The displacement $$(x)$$ of a point moving in a straight line is given by; $$x=8t^2-4t.$$ Then the velocity of the particle is zero at:

 1 $$0.4$$ s 2 $$0.25$$ s 3 $$0.5$$ s 4 $$0.3$$ s
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
87%
From NCERT
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The position of an object moving along the x-axis is given by, $$x=a+bt^2$$  where $$a=8.5$$ m, $$b=2.5$$ ms-2and $$t$$ is measured in seconds. Its velocity at $$t=2.0$$ s will be:
1. $$13$$ m/s
2. $$17$$ m/s
3. $$10$$ m/s
4. $$0$$

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
86%
From NCERT
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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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The position x of a particle moving along the x-axis varies with time t as x = $20\mathrm{t}$ $-$ $5{\mathrm{t}}^{2}$, where x is in meters and t is in seconds. The particle reverses its direction of motion at:

1. x = 40 m

2. x = 10 m

3. x = 20 m

4. x = 30 m

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
80%
From NCERT
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The position of an object moving along the x-axis is given by $$x = a+bt^{2}$$ where $$a=10$$ m, $$b=2$$ ms-2 and $$t$$ is in seconds. The velocity at $$t=3.0$$ s is:
1. $$12$$ ms-1
2. $$20$$ ms-1
3. $$36$$ ms-1
4. $$46$$ ms-1
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
79%
From NCERT
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A body in one-dimensional motion has zero speed at an instant. At that instant, it must have:

 1 zero velocity. 2 zero acceleration. 3 non-zero velocity. 4 non-zero acceleration.
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
72%
From NCERT
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Which of the following four statements is false?

 1 A body can have zero velocity and still be accelerated. 2 A body can have a constant velocity and still have a varying speed. 3 A body can have a constant speed and still have a varying velocity. 4 The direction of the velocity of a body can change when its acceleration is constant.

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
65%
From NCERT
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The position-time $$(x-t)$$ graphs for two children $$A$$ and $$B$$ returning from their school O to their homes P and Q respectively are shown in the graph. Choose the incorrect statement.

 1 $$B$$ reaches home faster than $$A.$$ 2 $$B$$ overtakes $$A$$ on the road twice. 3 $$B$$ walks faster than $$A.$$ 4 $$A$$ lives closer to the school than $$B.$$

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
60%
From NCERT
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If in one-dimensional motion, instantaneous speed $$v$$ satisfies $$0\leq v<v_0$$, then:

 1 the displacement in time $$T$$ must always take non-negative values. 2 the displacement $$x$$ in time $$T$$ satisfies  $$-\mathrm{v_0T} \lt x \lt \mathrm{v_0T}$$. 3 the acceleration is always a non-negative number. 4 the motion has no turning points.

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
54%
From NCERT
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