# A particle moving in unidirectional motion travels half of the total distance with a constant speed of $$15$$ m/s. Now the first half of the remaining journey time, it travels at $$10$$ m/s, and the second half of the remaining journey time, it travels at $$5$$ m/s. The average speed of the particle is: 1. $$12$$ m/s 2. $$10$$ m/s 3. $$7$$ m/s 4. $$15$$ m/s

Subtopic:  Average Speed & Average Velocity |
71%
From NCERT
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Two buses $$P$$ and $$Q$$ start from a point at the same time and move in a straight line and their positions are represented by $$X_p(t)=\alpha t+\beta t^2$$ and $$X_{Q}(t)=ft-t^2$$. At what time, do both the buses have the same velocity?
1. $$\frac{\alpha-f}{1+\beta}$$
2. $$\frac{\alpha+f}{2(\beta-1)}$$
3. $$\frac{\alpha+f}{2(1+\beta)}$$
4. $$\frac{f-\alpha}{2(1+\beta)}$$
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 $$a=10$$ 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 |
80%
From NCERT
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A particle is thrown vertically upward. Its velocity at half of the height is $$10$$ m/s, then the maximum height attained by it is: ($$g=10$$ m/s2)
1. $$8$$ m
2. $$20$$ m
3. $$10$$ m
4. $$16$$ m
Subtopic:  Uniformly Accelerated Motion |
80%
From NCERT
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Given below are two statements:
 Assertion (A): If the average velocity of a particle is zero in a time interval, it is possible that the instantaneous velocity is never zero in the interval. Reason (R): If the average velocity of a particle moving on a straight line is zero in a time interval then at least for one moment the instantaneous velocity will also be zero in the interval.
 1 Both (A) and (R) are True and (R) is the correct explanation of (A). 2 Both (A) and (R) are True but (R) is not the correct explanation of (A). 3 (A) is True but (R) is False. 4 Both (A) and (R) are False.
Subtopic:  Average Speed & Average Velocity |
From NCERT
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Select the correct option based on the statements given below:
 Assertion (A): A body can have acceleration even if its velocity is zero at a given instant of time. Reason (R): A body is momentarily at rest when it reverses its direction of motion.

 1 Both (A) and (R) are True and (R) is the correct explanation of (A). 2 Both (A) and (R) are True but (R) is not the correct explanation of (A). 3 (A) is True but (R) is False. 4 Both (A) and (R) are False.
Subtopic:  Uniformly Accelerated Motion |
60%
From NCERT
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Given below are two statements:
 Assertion (A): A particle having zero acceleration must have a constant speed. Reason (R): A particle having constant speed must have zero acceleration.

 1 Both (A) and (R) are True and (R) is the correct explanation of (A). 2 Both (A) and (R) are True but (R) is not the correct explanation of (A). 3 (A) is True but (R) is False. 4 Both (A) and (R) are False.
Subtopic:  Acceleration |
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Given below are two statements:
 Assertion (A): Adding a scalar to a vector of the same dimension is a meaningful algebraic operation. Reason (R): Displacement can be added to distance.

 1 Both (A) and (R) are True and (R) is the correct explanation of (A). 2 Both (A) and (R) are True but (R) is not the correct explanation of (A). 3 (A) is True but (R) is False. 4 Both (A) and (R) are False.
Subtopic:  Distance & Displacement |
68%
From NCERT
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The displacement-time $$(s\text-t)$$ graphs of two moving particles $$A~\text{and}~B$$ make angles of $$30^\circ$$ and $$45^\circ$$ with the $$x\text-$$axis as shown in the figure. The ratio of their respective velocity $$\left(\dfrac{v_A}{v_B}\right)$$ is:

 1 $$1: \sqrt{3}$$ 2 $$\sqrt{3}: 1$$ 3 $$1:1$$ 4 $$1:2$$
Subtopic:  Graphs |
71%
From NCERT
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A particle is moving along a straight line such that its position depends on time as $$x=1-at+bt^{2}$$, where $$a=2~\text{m/s}$$, $$b=1~\text{m/s}^2$$. The distance covered by the particle during the first $$3$$ seconds from start of the motion will be:

 1 $$2~\text{m}$$ 2 $$5~\text{m}$$ 3 $$7~\text{m}$$ 4 $$4~\text{m}$$
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
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