# A particle moves with a velocity $$v = αt^{3}$$ along a straight line. The average speed in time interval $$t=0$$ to $$t=T$$ will be: 1. $$\alpha T^3$$ 2. $$\frac{αT^{3}}{2}$$ 3. $$\frac{\alpha T^3}{3}$$ 4. $$\frac{αT^{3}}{4}$$

Subtopic:  Average Speed & Average Velocity |
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The position ($$x$$) of a particle in a straight line motion is given by $$x = 2 + 10 t - 5 t^{2}~\text{m}$$. Its velocity ($$v$$) is best represented by?

 1 2 3 4
Subtopic:  Graphs |
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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 |
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A body is moving along a straight line according to the equation of motion, $$x= t^{2} - 3 t + 4$$, where $$x$$ is in metre and $$t$$ is in seconds. What is the acceleration of the body when it comes to rest?
1. zero
2. $$2~\text{m/s}^2$$
3. $$\frac{3}{2}~\text{m/s}^2$$
4. $$1~\text{m/s}^2$$

Subtopic:  Acceleration |
84%
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A particle is allowed to fall from rest from a height $$h$$. Which of the following represents its velocity versus time graph?

 1 2 3 4

Subtopic:  Uniformly Accelerated Motion |
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A particle is moving along the positive $$x$$-axis with some initial velocity. The acceleration-time graphs are shown. In which case the velocity of the particle will increase for the entire time between $$t_1$$ and $$t_2$$?

 1 only in (II) 2 in (I) and (III) 3 in (I) and (II) 4 in (I), (II) and (III)

Subtopic:  Graphs |
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The graph below shows position as a function of time for two trains running on parallel tracks.

Which of the following statements is true?

 1 At time $$t_B$$ both the trains have the same velocity 2 Both the trains have the same velocity at some time after $$t_B$$ 3 Both the trains have the same velocity at some time before $$t_B$$ 4 Both the trains have the same acceleration
Subtopic:  Graphs |
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Two stones are thrown vertically up simultaneously with different velocities. Which of the following graphs represents the relative separation $$(\Delta y)$$ between them as a function of time $$(t)$$?

 1 2 3 4
Subtopic:  Graphs |
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The velocity $$v$$ of an object varies with its position $$x$$ on a straight line as $$v=3\sqrt{x}.$$ Its acceleration versus time $$(a\text-t)$$ graph is best represented by:

 1 2 3 4
Subtopic:  Acceleration |
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Starting from rest, a car accelerates uniformly at the rate of $$1~\text{m/s}^2$$ for some time, then decelerates uniformly at the rate of $$2~\text{m/s}^2$$ and finally comes to rest after a journey of $$1$$ minute. The maximum possible speed of the car during this journey is:
1. $$10$$ m/s
2. $$20$$ m/s
3. $$30$$ m/s
4. $$40$$ m/s

Subtopic:  Uniformly Accelerated Motion |
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