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. \(\sqrt{3}:\sqrt{2}:1\)$\mathrm{}$

For the given acceleration \(\left ( a \right )\) versus time \(\left ( t \right )\) graph of a body, the body is initially at rest.

From the following, the velocity \(\left ( v \right )\) versus time \(\left ( t \right )\) graph will be:

1.		2.
3.		4.

A particle moves with a velocity \(v = αt^{3}\) along a straight line. The average speed in time interval \(t=0\) to \(t=T\) will be:
1. \(\alpha T^3\)
2. \(\frac{αT^{3}}{2}\)
3. \(\frac{\alpha T^3}{3}\)
4. \(\frac{αT^{3}}{4}\)

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.

A boy falls from a building of height \(320\) m. After \(5\) seconds, superman jumps downward with initial speed \(u\) such that the boy can be saved. The minimum value of \(u\) is: (assume \(g= 10~\text{m/s}^2\)${\mathrm{}}^{}$)

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:

A body is moving along a straight line according to the equation of motion, \(x= t^{2} - 3 t + 4\), where \(x\) is in metre and \(t\) is in seconds. What is the acceleration of the body when it comes to rest?

A particle is allowed to fall from rest from a height \(h\). Which of the following represents its velocity versus time graph?

1.		2.
3.		4.

The graph below shows position as a function of time for two trains running on parallel tracks.

    
Which of the following statements is true?