The displacement of a particle is proportional to the cube of the time elapsed. How does the acceleration of the particle depends on time obtained?

1. \(𝑎 ∝ t^ 2 \)
2. \(𝑎 ∝ 𝑡^ 4 \)
3. \(𝑎 ∝ 𝑡 ^3\)
4. \(𝑎 ∝ 𝑡  \)

Starting from rest, the acceleration of a particle is \(𝑎 = 2 ( 𝑡 − 1 )\). The velocity of the particle at \(𝑡 = 5\ \text{𝑠}\) is:

1.  \(15\ \text{m/s}\)
2.  \(25\ \text{m/s}\)
3.  \(5\ \text{m/s}\)
4.  None of these

A particle moves along the x-axis as \({x}=4({t}-2)+{a}({t}-2)^2.\)Which of the following is true? 

A \(210\) meter long train is moving due north at a speed of \(25\ \text{m/s}\). A small bird is flying due South a little above the train with a speed of \(5\ \text{m/s}\). The time taken by the bird to cross the train is:

1. \(6\ \text{s}\)
2. \(7\ \text{s}\)
3. \(9\ \text{s}\)
4. \(10\ \text{s}\)

A ball is dropped on the floor from a height of 10 m. It rebounds to a height of 2.5 m. If the ball is in contact with the floor for 0.01 sec, the average acceleration during contact is 

1. 2100 m/sec² downwards

2. 2100 m/sec² upwards

3. 1400 m/sec²

4. 700 m/sec²

A ball is released from the top of a tower of height h meters. It takes T seconds to reach the ground. What is the position of the ball in T/3 seconds? 

1. h/9 meters from the ground

2. 7h/9 meters from the ground

3. 8h/9 meters from the ground

4. 17h/18 meters from the ground

A particle moving in a straight line covers half the distance with a speed of \(3~\text{m/s}\). The other half of the distance is covered in two equal time intervals with speeds of \(4.5~\text{m/s}\) and \(7.5~\text{m/s}\) respectively. The average speed of the particle during this motion is:
1. \(4.0~\text{m/s}\)
2. \(5.0~\text{m/s}\)
3. \(5.5~\text{m/s}\)
4. \(4.8~\text{m/s}\)

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. $ut$

A particle moves along the sides \(AB,BC,CD\) of a square of side \(25~\text{m}\) with a speed of \(15~\text{ms}^{-1}\). Its average velocity is:

1. \(15~\text{ms}^{-1}\)
2. \(10~\text{ms}^{-1}\)
3. \(7.5~\text{ms}^{-1}\)
4. \(5~\text{ms}^{-1}\)

A body has speed V, 2V and 3V in first 1/3 of distance S, second 1/3 of S and third 1/3 of S respectively. Its average speed will be

1. V

2. 2V

3. $\frac{18}{11}V$

4. $\frac{11}{18}V$