# 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–2, and $$t$$ 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 |
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When brakes are applied to a moving vehicle, the distance it travels before stopping is called stopping distance. It is an important factor for road safety and depends on the initial velocity $${v_0}$$ and the braking capacity, or deceleration, $$-a$$ that is caused by the braking. Expression for stopping distance of a vehicle in terms of $${v_0}$$ and $$a$$ is:

 1 $$\dfrac{{v_o}^2}{2a}$$ 2 $$\dfrac{{v_o}}{2a}$$ 3 $$\dfrac{{v_o}^2}{a}$$ 4 $$\dfrac{2a}{{v_o}^2}$$
Subtopic:  Acceleration |
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If a body travels some distance in a given time interval, then for that time interval, its:

 1 Average speed  ≥  |Average velocity| 2 |Average velocity|  ≥  Average speed 3 Average speed < |Average velocity| 4 |Average velocity| must be equal to average speed.

Subtopic:  Average Speed & Average Velocity |
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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 |
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AIPMT - 2005
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The figure shows the displacement-time graph of a particle moving on the x-axis. Then,

 1 the particle is continuously going in a positive x-direction. 2 the particle is at rest. 3 the velocity increases up to a time $$t_0$$, and then becomes constant. 4 the particle moves at a constant velocity up to a time $$t_0$$, and then stops.

Subtopic:  Graphs |
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A stone is released from an elevator going up with an acceleration $$a.$$ The acceleration of the stone after the release is:
1. $$a$$ upward
2. $$(g-a)$$ upward
3. $$(g-a)$$ downward
4. $$g$$ downward

Subtopic:  Uniformly Accelerated Motion |
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Mark the correct statements for a particle going on a straight line:

 (a) if the velocity and acceleration have opposite sign, the object is slowing down. (b) if the position and velocity have opposite sign, the particle is moving towards the origin. (c) if the velocity is zero at an instant, the acceleration should also be zero at that instant. (d) if the velocity is zero for a time interval, the acceleration is zero at any instant within the time interval.

Choose the correct option:

 1 (a), (b) and (c) 2 (a), (b) and (d) 3 (b), (c) and (d) 4 all of these

Subtopic:  Acceleration |
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A boy throws a ball straight up the side of a building and receives it after $$4$$ s. On the other hand, if he throws it so that it strikes a ledge on its way up, it returns to him after $$3$$ s. The ledge is at a distance $$d$$ below the highest point, where $$d=?$$ (take acceleration due to gravity, $$g=10$$ m/s2)
1. $$5$$ m
2. $$2.5$$ m
3. $$1.25$$ m
4. $$10$$ m

Subtopic:  Distance & Displacement |
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The study of motion of objects, without consideration of its cause, is:
1. statics
2. kinematics
3. mechanics
4. dynamics
Subtopic:  Distance & Displacement |
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The location of a particle is changed. What can we say about the displacement and distance covered by the particle?

 1 Both cannot be zero. 2 One of the two may be zero. 3 Both must be zero. 4 If one is positive, the other is negative, and vice-versa.
Subtopic:  Distance & Displacement |
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