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:

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.	\(t_1=t_2 \)

Which of the following four statements is false?

Two cars \(A\) and \(B\) are travelling in the same direction with velocities \(v_1\) and \(v_2\) \((v_1>v_2).\) When the car \(A\) is at a distance \(d\) behind the car \(B,\) the driver of the car \(A\) applied the brake producing uniform retardation \(a.\) There will be no collision when:
1. \(d < \frac{\left( v_{1} - v_{2} \right)^{2}}{2 a}\)

2. \(d < \frac{v_{1}^{2} - v_{2}^{2}}{2 a}\)

3. \(d > \frac{\left(v_{1} - v_{2}\right)^{2}}{2 a}\)

4. \(d > \frac{v_{1}^{2} - v_{2}^{2}}{2 a}\)

A particle moves a distance \(x\) in time \(t\) according to equation \(x = (t+5)^{-1}\). The acceleration of the particle is proportional to: 

The position \(x\) of a particle moving along the \(x\)-axis varies with time \(t\) as \(x=20t-5t^2,\) where \(x\) is in meters and \(t\) is in seconds. The particle reverses its direction of motion at:
1. \(x=40~\text{m}\)
2. \(x=10~\text{m}\)
3. \(x=20~\text{m}\)
4. \(x=30~\text{m}\)

A body starting from rest moves with uniform acceleration on a horizontal surface. The body covers \(3\) consecutive equal distances from the beginning in time \(t_1, t_2,\text{and}~t_3\)${\mathrm{}}_{}$ seconds. The ratio of \(t_1:t_2:t_3\) is:
1. \(1:2:3\)
2. \(1:\sqrt{2}:\sqrt{3}\)
3. \(1:\left(\sqrt{2}-1\right):\left(\sqrt{3}-\sqrt{2}\right)\)
4. \(\sqrt{3}:\sqrt{2}:1\)$\mathrm{}$

The position (\(x\)) of a particle in a straight line motion is given by \(x = 2 + 10 t - 5 t^{2}~\text{m}\). Its velocity (\(v\)) is best represented by?

1.		2.
3.		4.

An elevator whose floor-to-ceiling height is \(12\) meters, moves upward with an acceleration of \(2.2~\text{m/s}^2.\) After \(1.5~\text s\) since starting, a bolt falls from its ceiling. The time taken by the bolt to reach the floor is:
1. \(1~\text{s}\)
2. \(2~\text{s}\)
3. \(\sqrt{2}~\text{s}\)
4. \(\sqrt{3}~\text{s}\)

The displacement \((x)\) of a point moving in a straight line is given by; \(x=8t^2-4t.\) Then the velocity of the particle is zero at: