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. | \(20~\text{m/s}\) |
1. | \(\dfrac{1}{v} = \dfrac{1}{v_1}+\dfrac{1}{v_2}\) | 2. | \(\dfrac{2}{v} = \dfrac{1}{v_1}+\dfrac{1}{v_2}\) |
3. | \(\dfrac{v}{2} = \dfrac{v_1+v_2}{2}\) | 4. | \(v = \sqrt{v_1v_2}\) |
1. | \(t_1<t_2 \) or \(t_1>t_2 \) depending upon whether the lift is going up or down. |
2. | \(t_1<t_2 \) |
3. | \(t_1>t_2 \) |
4. | \(t_1=t_2 \) |
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.
2.
3.
4.
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:
1. | \(10\) m/s2 | 2. | \(32\) m/s2 |
3. | \(23\) m/s2 | 4. | \(16\) m/s2 |
The displacement \(x\) of a particle varies with time \(t\) as \(x = ae^{-\alpha t}+ be^{\beta t}\), where \(a,\) \(b,\) \(\alpha,\) and \(\beta\) are positive constants. The velocity of the particle will:
1. | \(\alpha\) and \(\beta.\) | be independent of
2. | go on increasing with time. |
3. | \(\alpha=\beta.\) | drop to zero when
4. | go on decreasing with time. |
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; . Its displacement, when its velocity is zero will be:
1. \(2\) m
2. \(4\) m
3. \(0\) m
4. none of the above