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

1. $a\propto t^2$

2. $a\propto t^4$

3. $a\propto t^3$

4. $a\propto t$ 

Starting from rest, acceleration of a particle is $a=2(t-1).$ The velocity of the particle at $t=5s$ is:

1.  15 m/sec
2.  25 m/sec
3.  5 m/sec
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 m/s. A small bird is flying due South a little above the train with a speed of 5m/s. The time taken by the bird to cross the train is 

1. 6 s

2. 7 s

3. 9 s

4. 10 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. $\frac{11}{18}V$