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1. Given below are two statements:

Assertion (A):	If the average velocity of a particle over a certain time interval is zero, it is possible that the instantaneous velocity of the particle is never zero during that interval.
Reason (R):	For a particle moving along a straight line, if its average velocity over a time interval is zero, then there must be at least one instant within that interval when the instantaneous velocity is zero.

 

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.

2.

A point moves in a straight line so that its displacement is \(x\) m at time \(t\) sec, given by ${\mathrm{}}^{}$\(x^2= t^2+1\). Its acceleration in \(\text{m/s}^2\) at time \(1\) sec is:
1. \(\frac{1}{x}\)
2. \(\frac{1}{x} - \frac{1}{x^{3}}\)
3. \(\frac{2}{x}\)
4. \(-\frac{t^2}{x^3}\)

3.

A ball is bouncing elastically with a speed of \(1~\text{m/s}\) between the walls of a railway compartment of size \(10~\text m\) in a direction perpendicular to the walls. The train is moving at a constant velocity of \(10~\text{m/s}\) parallel to the direction of motion of the ball. As seen from the ground:

(a)	the direction of motion of the ball changes every \(10\) sec.
(b)	the speed of the ball changes every \(10\) sec.
(c)	the average speed of the ball over any \(20\) sec intervals is fixed.
(d)	the acceleration of the ball is the same as from the train.

Choose the correct option:

1.	(a), (c), (d)	2.	(a), (c)
3.	(b), (c), (d)	4.	(a), (b), (c)

4. A rocket moves vertically up with a constant acceleration of \(8\) m/s². After sometime,  its fuel gets exhausted and it falls under gravity. If the maximum height attained by the rocket is \(180\) m, what was the speed when the fuel exhausted? 
1. \(30\) m/s
2. \(40\) m/s
3. \(60\) m/s
4. \(50\) m/s

5.

In the following displacement \((x)\) versus time \((t)\) graph, at which points \(P, Q\) and \(R\) will the object's speed be increasing?
       
1. \(R\) only
2. \(P\) only
3. \(Q\) and \(R\) only
4. \(P,Q,R\)