A ball is projected upwards from a height h above the surface of the earth with velocity v. The time at which the ball strikes the ground is

(1) $\frac{v}{g}+\frac{2hg}{\sqrt{2}}$

(2) $\frac{v}{g}\left[1-\sqrt{1+\frac{2h}{g}}\right]$

(3) $\frac{v}{g}\left[1+\sqrt{1+\frac{2gh}{v^2}}\right]$

(4) $\frac{v}{g}\left[1+\sqrt{v^2+\frac{2g}{h}}\right]$

A particle is dropped vertically from rest from a height. The time taken by it to fall through successive distances of \(1~\text{m}\) each will then be:

A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time (Given $g=9.8m/s^2)$

(1) At least 0.8 m/s

(2) Any speed less than 19.6 m/s

(3) Only with speed 19.6 m/s

(4) More than 19.6 m/s

If a ball is thrown vertically upwards with speed u, the distance covered during the last t seconds of its ascent is 

(1) $\frac{1}{2}g{t}^2$

(2) $ut-\frac{1}{2}g{t}^2$

(3) $(u-gt)t$

(4) $ut$

The variation of velocity of a particle with time moving along a straight line is illustrated in the following figure. The distance travelled by the particle in four seconds is 

1. 60 m

2. 55 m

3. 25 m

4. 30 m

The displacement of a particle as a function of time is shown in the figure. The figure shows that
                      
1. The particle starts with certain velocity but the motion is retarded and finally the particle stops
2. The velocity of the particle is constant throughout
3. The acceleration of the particle is constant throughout
4. The particle starts with constant velocity, then motion is accelerated and finally the particle moves with another constant velocity

A ball is thrown vertically upwards. Which of the following graph/graphs represent velocity-time graph of the ball during its flight (air resistance is neglected) 

1. a

2. b

3. c

4. d

The graph between the displacement \(x\) and time \(t\) for a particle moving in a straight line is shown in the figure.

During the interval OA, AB, BC and CD the acceleration of the particle is:

The v – t graph of a moving object is given in the figure. The maximum acceleration is:
                             
1.  $1cm/se{c}^2$
2.  $2cm/se{c}^2$
3.  $3cm/se{c}^2$
4.  $6cm/se{c}^2$

The displacement versus time graph for a body moving in a straight line is shown in the figure. Which of the following regions represents the motion when no force is acting on the body?

(1) ab

(2) bc

(3) cd

(4) de