Which one of the following displacement-time graph represents two moving objects \(P\) and \(Q\) with zero relative velocity?

1.		2.
3.		4.

The displacement-time graph for two particles A and B is as follows. The ratio $\frac{v_A}{v_B}$ is

(1) 1: 2

(2) 1: $\sqrt{3}$

(3) $\sqrt{3}$: 1

(4) 1: 3

For the acceleration-time \((a-t)\) graph shown in figure, the change in velocity of particle from \(t=0\) to \(t=6~\text s\) is

1. \(10~\text{m/s}\)
2. \(4~\text{m/s}\)
3. \(12~\text{m/s}\)
4. \(8~\text{m/s}\)

The velocity versus time graph of a body moving in a straight line is as shown in the figure below:

The acceleration-time graph for a particle is given in the figure. If it starts motion at \(t=0\), the distance travelled in \(3\) s will be:
      
1. \(4~\text{m}\)
2. \(2~\text{m}\)
3. \(0~\text{m}\)
4. \(6~\text{m}\)

Figure shows the position of a particle moving on the x-axis as a function of time

(1) The particle has come to rest 4 times

(2) The velocity at t = 8 s is negative

(3) The velocity remains positive for t = 2 s to t = 6 s

(4) The particle moves with a constant velocity

A particle moves along x-axis in such a way that its x co-ordinate varies with time according to the equation x = 4 - 2t + t². The velocity of the particle will vary with time as-

(1) 

(2) 

(3) 

(4) 

The position (x) of a particle moving along x-axis vares with time (t) as shown in figure. The average acceleration of particle in time interval t=0 to t=8 s is

(1) 3 m/s²

(2) - 5 m/s²

(3) - 4 m/s²

(4) 2.5 m/s²

The position (x)-time (t) graph for a particle moving along a straight line is shown in the figure. The average speed of particle in time interval t=0 to t=8 s is

(1) Zero 

(2) 5 m/s

(3) 7.5 m/s

(4) 9.7 m/s

A boat covers certain distance between two spots in a river taking t₁ hrs going downstream and t₂ hrs going upstream. What time will be taken by boat to cover same distance in still water?

(1) $\frac{t_1+t_2}{2}$

(2) $2\left(t_2-t_1\right)$

(3) $\frac{2t_1{t}_2}{t_1+t_2}$

(4) $\sqrt{t_1{t}_2}$