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. $\frac{11}{18}V$ 

The displacement of the particle varies with time according to the relation $\mathrm{x}=\frac{\mathrm{k}}{\mathrm{b}}[1-{\mathrm{e}}^{-\mathrm{bt}}]$. Then the velocity of the particle is

1. $k\left(e^{-bt}\right)$

2. $\frac{k}{b^2{e}^{-bt}}$

3. $kb{e}^{-bt}$

4. None of these 

A bullet moving with a velocity of 200 cm/s penetrates a wooden block and comes to rest after traversing 4 cm inside it. What velocity is needed for travelling distance of 9 cm in same block?

1. 100 cm/s

2. 136.2 cm/s

3. 300 cm/s

4. 250 cm/s

The speed of a body moving with uniform acceleration is u. This speed is doubled while covering a distance S. When it covers an additional distance S, its speed would become

1. $\sqrt{3}u$

2. $\sqrt{5}u$

3. $\sqrt{11}u$

4. $\sqrt{7}u$

A balloon rises from rest with a constant acceleration g/8. A stone is released from it when it has risen to height h. The time taken by the stone to reach the ground is

1. $4\sqrt{\frac{h}{g}}$

2. $2\sqrt{\frac{h}{g}}$

3. $\sqrt{\frac{2h}{g}}$

4. $\sqrt{\frac{g}{h}}$ 

A particle is projected upwards. The times corresponding to height \(h\) while ascending and while descending are t₁ and t₂ respectively. The velocity of projection will be:
1. \(gt_1\)
2. \(gt_2\)
3. \(g(t_1+t_2)\)
4. \(\frac{g(t_1+t_2)}{2}\)

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. \(4.8~\text{m/s}\)

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