Kinematics Of A Particle (1)

1. Particle A and B move as shown in figure. The minimum separation between A and B is :

10 m

7.92 m

0 m

8 m

We will analyze this relative to A.

A seen from A

Distance of B from A

Minimum value of =

Since D for

So, t and minimum value is 7.92 m

Explanation

We will analyze this relative to A.

A seen from A

Distance of B from A

Minimum value of =

Since D for

So, t and minimum value is 7.92 m

2. A stone is released from a elevator going up with an acceleration a. The acceleration of the stone after the released is :

A upward

(g - a) upward

G downward

After the stone released, only a downward force of mg acts on to it. So its acceleration is g downwards

Explanation

After the stone released, only a downward force of mg acts on to it. So its acceleration is g downwards

3. A person standing near the edge of the top of building throws two balls A and B. The ball A is thrown vertically downward with the same speed. The ball A hits the ground with a speed

and the ball b hits the ground with a speed

. We have

VA>VB

VA

VA=VB

The relation between VA and VB depends upon the height of the building

In both the cases use 3rd equation of motion.

Explanation

In both the cases use 3rd equation of motion.

4. Mark the correct statements :

The magnitude of the velocity of a particle is equal to its speed

The magnitude of average velocity in an interval is equal to its average speed in that interval

It is possible to have a situation in which the speed of a particle is never zero but the average speed is not zero

It is possible to have a situation in which the speed of the particle is never zero but the average speed is interval is zero

(A) is correct

(B) Avg. velocity and Avg speed

It is possible distance and displacement are not equal.

So Wrong

(C) As speed is zero always so distance traveled is 0 which means average speed must be 0

So Wrong

(D) As speed is non-zeroParticle covers some distance so average speed cannot be 0.

So Wrong

Explanation

(A) is correct

(B) Avg. velocity and Avg speed

It is possible distance and displacement are not equal.

So Wrong

(C) As speed is zero always so distance traveled is 0 which means average speed must be 0

So Wrong

(D) As speed is non-zeroParticle covers some distance so average speed cannot be 0.

So Wrong

5. The displace of a particle moving in a straight line is given by

. Here s is in m and t is in seconds. The distance covered by the particle is first 5 seconds is :

10 m

26 m

24 m

16 m

We are required to find the distance and not the displacement.

o, total distance = |displacement from t = 0 to 3s| + |displacement from t = 3s to 5s|

=

= (Particle turns around at t = 3s)

Explanation

We are required to find the distance and not the displacement.

o, total distance = |displacement from t = 0 to 3s| + |displacement from t = 3s to 5s|

=

= (Particle turns around at t = 3s)

6. A balloon starts rising from rest from the ground with an acceleration of 1.25 m/s². After 8s, a stone is released from the balloon. The stone will :

Cover a distance of 40 m

Have a displacement of 50 m

Reach the ground in 4s

Begin to move down after being released

The stone will reach the ground in 4 seconds because the acceleration due to gravity is constant and independent of the initial velocity of the stone. Therefore, the stone will fall with an acceleration of 9.8 m/s^2. Since the stone is released after 8 seconds, it will fall for an additional 4 seconds before reaching the ground.

Explanation

The stone will reach the ground in 4 seconds because the acceleration due to gravity is constant and independent of the initial velocity of the stone. Therefore, the stone will fall with an acceleration of 9.8 m/s^2. Since the stone is released after 8 seconds, it will fall for an additional 4 seconds before reaching the ground.

7. The figure shows, the displacement-time graph of a particle moving on the X-axis.

The particle is continuously going in positive x direction

The particle is at rest

The velocity increases up to a time , and then becomes constant

The particle moves at a constant velocity up to a time , and then stops

For time t
for time t > t0 velocity = slope of graph = 0

Explanation

For time t
for time t > t0 velocity = slope of graph = 0

8. Acceleration-velocity graph of a particle moving in a straight line is as shown in the figure. The slope of velocity-displacement graph is

Increases linearly

Decreases linearly

Is constant

Increases parabolically

a=kv
vdv/dx=kv
dv/dx=k
thus, slop =k, which is constant

Explanation

a=kv
vdv/dx=kv
dv/dx=k
thus, slop =k, which is constant

9. 6 particles A, B, C, D, E, F are located at the vertices of a regular hexagon of side d. All particles move with the same speed v such that the velocity of A is directed towards B, that of B towards C and so on (F is direction towards A). After what time will the particle meet ?

2d/v

3d/v

2d/3v

D/v

Sorry, no explanation at this point of time...

Explanation

Sorry, no explanation at this point of time...