A ball is thrown vertically downwards with a velocity of \(20\) m/s from the top of a tower. It hits the ground after some time with the velocity of \(80\) m/s . The height of the tower is: (assuming \(g = 10~\text{m/s}^2)\)$$

1.	\(340\) m	2.	\(320\) m
3.	\(300\) m	4.	\(360\) m

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. \(20~\text{m/s}\) 

A person travelling in a straight line moves with a constant velocity \(v_1\) for a certain distance \(x\) and with a constant velocity \(v_2\) ${\mathrm{}}_{}$for the next equal distance. The average velocity \(v\) is given by the relation:

A person standing on the floor of an elevator drops a coin. The coin reaches the floor in time $t_1$ if the elevator is moving uniformly and time $t_2$ if the elevator is stationary. Then:

A particle covers half of its total distance with speed ν₁ and the rest half distance with speed ν₂.
Its average speed during the complete journey is:

1. $\frac{v_1+v_2}{2}$

2. $\frac{v_1{v}_2}{v_1+v_2}$

3. $\frac{2v_1{v}_2}{v_1+v_2}$

4. $\frac{v_1^2{v}_2^2}{v_1^2+v_2^2}$

The motion of a particle is given by the equation \(S = \left(3 t^{3} + 7 t^{2} + 14 t + 8 \right) \text{m} ,\) The value of the acceleration of the particle at \(t=1~\text{s}\) is:

The displacement \(x\) of a particle varies with time \(t\) as \(x = ae^{-\alpha t}+ be^{\beta t}\)$\mathrm{}$
, where \(a,\) \(b,\) \(\alpha,\) and \(\beta\) are positive constants. The velocity of the particle will:

A car is moving with velocity v. It stops after applying breaks at a distance of 20 m. If the velocity of the car is doubled, then how much distance it will cover (travel) after applying breaks?
1.  40 m
2.  80 m
3.  160 m
4.  320 m

A body starts falling from height \(h\) and if it travels a distance of \(\frac{h}{2}\) during the last second of motion, then the time of flight is (in seconds):
1. \(\sqrt{2}-1\)
2. \(2+\sqrt{2}\)
3. \(\sqrt{2}+\sqrt{3}\)
4. \(\sqrt{3}+2\)

For a particle, displacement time relation is given by $t$ $=$ $\sqrt{x}$ $+$ $3$ . Its displacement, when its velocity is zero will be:
1. \(2\) m
2. \(4\) m
3. \(0\)
4. none of the above