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.

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

A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point:

         
1. B

2. C

3. D

4. A

A particle moves in a straight line, according to the law \(x=4a[t+asin(t/a)], \) where \(x\) is its position in metres, \(t\) is in seconds & \(a\) is some constant, then the velocity is zero at:

A point moves in a straight line so that its displacement is x m at time t sec, given by ${\mathrm{x}}^2={\mathrm{t}}^2+1$. Its acceleration in $\mathrm{m}/{\mathrm{s}}^2$ at time 1 sec is:

1.  $\frac{1}{\mathrm{x}}$

2.  $\frac{1}{\mathrm{x}}-\frac{1}{{\mathrm{x}}^3}$

3.  $\frac{2}{\mathrm{x}}$

4.  $-\frac{{\mathrm{t}}^2}{{\mathrm{x}}^3}$

The position x of a particle moving along the x-axis varies with time t as x = $20\mathrm{t}$ $-$ $5{\mathrm{t}}^2$, where x is in meters and t is in seconds. The particle reverses its direction of motion at:

1. x = 40 m

2. x = 10 m

3. x = 20 m

4. x = 30 m

Two cars A and B are travelling in the same direction with velocities v₁ and v₂ $(v_1>v_2)$. When the car A is at a distance d behind car B, the driver of the car A applied the brake producing uniform retardation a. There will be no collision when-

1. $d<\frac{{(v_1-v_2)}^2}{2a}$

2. $d<\frac{v_1^2-v_2^2}{2a}$

3. $d>\frac{{(v_1-v_2)}^2}{2a}$

4. $d>\frac{v_1^2-v_2^2}{2a}$ 

Which of the following four statements is false?

The initial velocity of a particle is u (at t = 0) and the acceleration f is given by at. Which of the following relation is valid?

1. $v=u+a{t}^2$

2. $v=u+a\frac{t^2}{2}$

3. $v=u+at$

4. v = u

A stone falls freely from rest from a height h and it travels a distance of $\frac{9h}{25}$ in the last second. The value of h is: