Assertion (A):	Displacement of a body may be zero when distance travelled by it is not zero.
Reason (R):	The displacement is the longest distance between initial and final position.

 

1.	Both (A) and (R) are True and (R) is the correct explanation of (A).
2.	Both (A) and (R) are True but (R) is not the correct explanation of (A).
3.	(A) is True but (R) is False.
4.	Both (A) and (R) are False.

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.

Assertion : The equation of motion can be applied only if acceleration is along the direction of velocity and is constant.

Reason : If the acceleration of a body is constant then its motion is known as uniform motion.

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

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 

A particle is moving in a straight line and passes through a point O with a velocity of 6 ms^–1. The particle moves with a constant retardation of 2 ms^–2 for 4 s and there after moves with constant velocity. How long after leaving O does the particle return to O

(1) 3s

(2) 8s

(3) Never

(4) 4s

A bird flies for 4 s with a velocity of $|t-2|m/s$ in a straight line, where t is time in seconds. It covers a distance of

1. 2 m

2. 4 m

3. 6 m

4. 8 m

A body is projected vertically up with a velocity v and after some time it returns to the point from which it was projected. The average velocity and average speed of the body for the total time of flight are

(1) $\overrightarrow{v}/2$ and v/2

(2) 0 and v/2

(3) 0 and 0

(4) $\overrightarrow{v}/2$ and 0

Two cars P and Q start from a point at the same time in a straight line and their positions are represented by $x_p\left(t\right)=at+b{t}^2$ and $x_Q\left(t\right)=ft-t^2$. At what time do the cars have the same velocity?

(1) $\frac{a-f}{1+b}$

(2)$\frac{a+f}{2\left(b-1\right)}$

(3) $\frac{a+f}{2\left(1+b\right)}$

(4) $\frac{f-a}{2\left(1+b\right)}$

A particle moves a distance \(x\) in time \(t\) according to equation \(x = (t+5)^{-1}\). The acceleration of the particle is proportional to: