# Kinematics Of A Particle (1)

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Kinematics or 1-d motions is an important syllabus for IIT-JEE.

• 1.

### 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 :

• A.

Cover a distance of 40 m

• B.

Have a displacement of 50 m

• C.

Reach the ground in 4s

• D.

Begin to move down after being released

C. Reach the ground in 4s
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.

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• 2.

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

• A.

The particle is continuously going in positive x direction

• B.

The particle is at rest

• C.

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

• D.

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

C. The velocity increases up to a time , and then becomes constant
Explanation
For time t < t0 velocity of particle = constant positive value

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

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• 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

• A.

VA>VB

• B.

VA

• C.

VA=VB

• D.

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

C. VA=VB
Explanation
In both the cases use 3rd equation of motion.

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• 4.

### 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 :

• A.

10 m

• B.

26 m

• C.

24 m

• D.

16 m

B. 26 m
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)

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• 5.

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

• A.

A upward

• B.

(g - a) upward

• C.

(g - a) upward

• D.

g downward

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

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• 6.

### 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 ?

• A.

2d/v

• B.

3d/v

• C.

2d/3v

• D.

D/v

A. 2d/v
Explanation
Sorry, no explanation at this point of time...

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• 7.

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

• A.

Increases linearly

• B.

Decreases linearly

• C.

is constant

• D.

increases parabolically

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

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• 8.

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

• A.

10 m

• B.

7.92 m

• C.

0 m

• D.

8 m

B. 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

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• 9.

### An object may have

• A.

Varying speed without having varying velocity

• B.

Varying velocity without having varying speed

• C.

Nonzero acceleration without having varying velocity

• D.

Nonzero acceleration without varying speed

B. Varying velocity without having varying speed
D. Nonzero acceleration without varying speed
Explanation
(A) Not possible So wrong

(B) Uniform circular motion So wrong

(C) Not possible So wrong

(D) Possiblein uniform circular motion. Correct

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• 10.

### Mark the correct statements :

• A.

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

• B.

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

• C.

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

• D.

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

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• Current Version
• Mar 13, 2024
Quiz Edited by
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• Aug 27, 2011
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