Read the assertion and reason carefully to mark the correct option out of the options given below:

(1) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.

(3) If assertion is true but reason is false.

(4) If the assertion and reason both are false.

(5) If assertion is false but reason is true.

Assertion : The average and instantaneous velocities have same value in a uniform motion.

Reason : In uniform motion, the velocity of an object increases uniformly.

A car travels a distance S on a straight road in two hours and then returns to the starting point in the next three hours. Its average velocity is

(1) S/5

(2) 2S/5

(3) S/2 + S/3

(4) None of the above

A particle moves along the sides AB, BC, CD of a square of side 25 m with a velocity of 15 ms^-1. Its average velocity is

(1) 15 ms^-1

(2) 10 ms^-1

(3) 7.5 ms^-1

(4) 5 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 

The acceleration of a particle starting from rest varies with time according to the relation A = – aω²sinωt. The displacement of this particle at a time t will be:

1. $-\frac{1}{2}\left({\mathrm{a\omega }}^2\mathrm{sin\omega t}\right){\mathrm{t}}^2$

2. $\mathrm{a\omega sin\omega t}$

3. $\mathrm{a\omega cos\omega t}$

4. $\mathrm{asin\omega t}$

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 ms^–1. A policeman chases him on a motor cycle moving at a speed of 10 ms^–1. 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?

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