If in one-dimensional motion, instantaneous speed \(v\) satisfies \(0\leq v<v_0\), then:

1.	the displacement in time \(T\) must always take non-negative values.
2.	the displacement \(x\) in time \(T\) satisfies  \(-\mathrm{v_0T} \lt x \lt \mathrm{v_0T}\).
3.	the acceleration is always a non-negative number.
4.	the motion has no turning points.

A vehicle travels half the distance \(\mathrm{L} \) with speed \(\mathrm{v_1}\) and the other half with speed \(\mathrm{v_2},\) then its average speed is:
1. $\frac{{\mathrm{v}}_1+{\mathrm{v}}_2}{2}$

2. $\frac{2{\mathrm{v}}_1+{\mathrm{v}}_2}{{\mathrm{v}}_1+{\mathrm{v}}_2}$

3. $\frac{2{\mathrm{v}}_1{\mathrm{v}}_2}{{\mathrm{v}}_1+{\mathrm{v}}_2}$

4. $\frac{\mathrm{L}({\mathrm{v}}_1+{\mathrm{v}}_2)}{{\mathrm{v}}_1{\mathrm{v}}_2}$

The displacement of a particle is given by x = ${(\mathrm{t} - 2)}^2$ where x is in meters and t in seconds. The. distance covered by the particle in the first 4 seconds is

1. 4 m
2. 8 m
3. 12 m
4. 16 m

At a metro station, a girl walks up a stationary escalator in time ${\mathrm{}}_{}$\(t_1\). If she remains stationary on the escalator, then the escalator takes her up in time \(t_2\). The time taken by her to walk upon the moving escalator will be:
1. \( \left(\mathrm{t}_1+\mathrm{t}_2\right) / 2\)
2. \( \mathrm{t}_1 \mathrm{t}_2 /\left(\mathrm{t}_2-\mathrm{t}_1\right)\)
3. \( \mathrm{t}_1 \mathrm{t}_2 /\left(\mathrm{t}_1+\mathrm{t}_2\right) \)
4. \( \mathrm{t}_1-\mathrm{t}_2\)

The variation of quantity A with quantity B is plotted in the given figure which describes the motion of a particle in a straight line.
           
Consider the following statements:

Select the correct option:

A graph of x versus t is shown in the figure.

(a) The particle was released from rest at t = 0.
(b) At B, the acceleration a > 0.
(c) Average velocity for the motion between A and D is positive.
(d) The speed at D exceeds that at E.

Choose the correct alternatives:

1. (b, d)

2. (a, b)

3. (b, c)

4. (a, d)

For the one-dimensional motion, described by x = t - sint, the following statements are given.

(a) x(t) > 0 for all t > 0
(b) v(t) > 0 for all t > 0
(c) a(t) > 0 for all t > 0
(d) v(t) lies between 0 and 2

Choose the correct option:

1. (a, c)

2. (b, c)

3. (a, d)

4. (b, d)

A ball is bouncing elastically with a speed of 1 m/s between the walls of a railway compartment of size 10 m in a direction perpendicular to the walls. The train is moving at a constant velocity of 10 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)

A lift is coming from the 8th floor and is just about to reach the 4th floor. Taking the ground floor as the origin and positive direction upwards for all quantities, which one of the following is correct:

Among the four graphs shown in the figure, there is only one graph for which average velocity over the time interval \((0,T)\) can vanish for a suitably chosen \(T\). Select the graph.

1.		2.
3.		4.