A person sitting on the ground floor of a building notices through the window, of height \(1.5~\text{m}\), a ball dropped from the roof of the building crosses the window in \(0.1~\text{s}\). What is the velocity of the ball when it is at the topmost point of the window? \(\left(g = 10~\text{m/s}^2\right )\)
1. \(15.5~\text{m/s}\)
2. \(14.5~\text{m/s}\)
3. \(4.5~\text{m/s}\) 
4. \(20~\text{m/s}\) 

Refer to the graph in the figure. Match the following.

Graph        Characteristics

         (i) has v > 0 and a < 0 throughout

         (ii) has x > 0 throughout and has a point with v = 0 and a point with a = 0

         (iii) has a point with zero displacement for t > 0

         (iv) has v < 0 and a > 0

$\left(1\right) \left(\mathrm{a}\right)-\left(\mathrm{ii}\right), \left(\mathrm{b}\right)-\left(\mathrm{iii}\right), \left(\mathrm{c}\right)-\left(\mathrm{i}\right), \left(\mathrm{d}\right)-\left(\mathrm{iv}\right)$
$\left(2\right) \left(\mathrm{a}\right)-\left(\mathrm{iv}\right), \left(\mathrm{b}\right)-\left(\mathrm{ii}\right), \left(\mathrm{c}\right)-\left(\mathrm{iii}\right), \left(\mathrm{d}\right)-\left(\mathrm{i}\right)$
$\left(3\right) \left(\mathrm{a}\right)-\left(\mathrm{iii}\right), \left(\mathrm{b}\right)-\left(\mathrm{ii}\right), \left(\mathrm{c}\right)-\left(\mathrm{iv}\right), \left(\mathrm{d}\right)-\left(\mathrm{i}\right)$
$\left(4\right) \left(\mathrm{a}\right)-\left(\mathrm{i}\right), \left(\mathrm{b}\right)-\left(\mathrm{ii}\right), \left(\mathrm{c}\right)-\left(\mathrm{iii}\right), \left(\mathrm{d}\right)-\left(\mathrm{iv}\right)$

This objective question is based on NCERT Exemplar subjective Question.

A uniformly moving cricket ball is turned back by hitting it with a bat for a very short time interval. The variation of its acceleration with time is:

(Take acceleration in the backward direction as positive)

1. 

2. 

3. 

4. 

This objective question is based on NCERT Exemplar subjective Question.

The motion of a particle is represented by $\mathrm{x}\left(\mathrm{t}\right)=\mathrm{t}-\mathrm{sint}$. Then,

(1) the particle moving along negative x-direction comes to rest periodically and moves forward.

(2) the particle moving along x-direction comes to rest periodically and moves backwards.

(3) the particle moving along positive x-direction comes to rest periodically and moves forward.

(4) the particle moving along x-direction comes to rest periodically and moves either backwards or forwards.

This objective question is based on NCERT Exemplar subjective Question.

The position of an object is given by $\mathrm{x}\left(\mathrm{t}\right) = \mathrm{A}+{\mathrm{Be}}^{-\mathrm{\gamma t}}, \mathrm{where} \mathrm{A}>\mathrm{B} \mathrm{and} \mathrm{\gamma }>0$, then at any time t:

(1) x < 0, v > 0, a > 0

(2) x > 0, v < 0, a > 0

(3) x < 0, v < 0, a < 0

(4) x < 0, v > 0, a > 0

This objective question is based on NCERT Exemplar subjective Question.

An object falling through a fluid is observed to have acceleration given by a = g - bv, where g = gravitational acceleration and b, is constant. After a long time of release, it is observed to fall with constant speed. The value of constant speed is:

$\left(1\right) \frac{\mathrm{g}}{\mathrm{b}}$
$\left(2\right) \frac{\mathrm{g}}{{\mathrm{b}}^2}$
$\left(3\right) \frac{{\mathrm{g}}^2}{\mathrm{b}}$
$\left(4\right) \sqrt{\frac{\mathrm{g}}{\mathrm{b}}}$

This objective question is based on NCERT Exemplar subjective Question.

A ball is dropped and its displacement versus time graph is as shown. (Displacement x from the ground and all quantities are positive upwards).

The velocity-time graph of the ball is given by:

1. 

2. 

3. 

4. 

This objective question is based on NCERT Exemplar subjective question.

A car is moving along a straight line, say OP in the figure. It moves from O to P in 18 s and returns from P to Q in 6.0 s. The average velocity and average speed of the car in going from O to P and back to Q respectively are:

1.  10 m/s & 10 m/s

2.  20 m/s & 30 m/s 

3.  20 m/s & 20 m/s

4.  10 m/s & 20 m/s

The position of an object moving along \(\mathrm{x}\)-axis is given by \(x=a+bt^2\), where \(a=8.5\) m, \(b=2.5\) ${\mathrm{ms}}^{-2}$ and \(t\) is measured in seconds. Its average velocity between \(t=2.0\) s and \(t=4.0\) s is:
1. \(10\) m/s
2. \(15\) m/s
3. \(20\) m/s
4. \(25\) m/s

Which of the following does not represent the equation of motion for constant acceleration?
1. \(v=v_0+at\)
2. \(v^2=v_0^2+2a(x-x_0)\)
3. \(x = x_0v_0+\frac{1}{2}at^2\)
4. \(x = x_0+v_0t+\frac{1}{2}at^2\)