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. $\frac{11}{18}V$ 

If the body covers one-third distance at speed v₁, next one third at speed v₂ and last one third at speed v₃, then average speed will be

1. $\frac{v_1{v}_2+v_2{v}_3+v_3{v}_1}{v_1+v_2+v_3}$

2. $\frac{v_1+v_2+v_3}{3}$

3. $\frac{v_1{v}_2{v}_3}{v_1{v}_2+v_2{v}_3+v_3{v}_1}$

4. $\frac{3v_1{v}_2{v}_3}{v_1{v}_2+v_2{v}_3+v_3{v}_1}$  

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 

If the velocity of a particle is (10 + 2t²) m/s, then the average acceleration of the particle between 2 sec and 5 sec is:

1. 2 m/s²

2. 4 m/s²

3. 12 m/s²

4. 14 m/s²

A thief is running away on a straight road in a jeep moving with a speed of $9$ m/s. A policeman chases him on a motorcycle moving at a speed of $10$ m/s. If the instantaneous separation of the jeep from the motorcycle is $100$ m, how long will it take for the policeman to catch the thief?
1. $1$ s
2. $19$ s
3. $90$ s
4. $100$ s

A car A is travelling on a straight level road with a uniform speed of 60 km/h. It is followed by another car B which is moving with a speed of 70 km/h. When the distance between them is 2.5 km, the car B is given a deceleration of 20 km/h². After how much time will B catch up with A

1. 1 hr

2. 1/2 hr

3. 1/4 hr

4. 1/8 hr

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. $\sqrt{7}u$

Two trains one of length 100 m and another of length 125 m, are moving in mutually opposite directions along parallel lines, meet each other, each with speed 10 m/s. If their acceleration are 0.3 m/s² and 0.2 m/s² respectively, then the time they take to pass each other will be

1.  5 s
2.  10 s
3.  15 s
4.  20 s