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HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1 | HC Verma Solutions - JEE PDF Download

Short Answers

Q.1. Galileo was punished by the Church for teaching that the sun is stationary and the earth moves around it. His opponents held the view that the earth is stationary and the sun moves around it. If the absolute motion has no meaning, are the two viewpoints not equally correct or equally wrong?

The absolute motion has no meaning. In the relative motion view, the two viewpoints are the same. Hence, both viewpoints are equally correct or equally wrong.


Q.2. When a particle moves with constant velocity, its average velocity, its instantaneous velocity and its speed are all equal. Comment on this statement.

Constant velocity means that a particle has the same direction and speed at every point. So, its average velocity and instantaneous velocity are equal. Its speed being a scalar quantity is equal in magnitude only.


Q.3. A car travels at a speed of 60 km/hr due north and the other at a speed of 60 km/hr due east. Are the velocities equal? If no, which one is greater? If you find any of the questions irrelevant, explain. 

No, as the directions of the cars are different, their velocities are not equal, as velocity is a vector quantity.
We cannot compare velocities on the basis of direction only, so the question is irrelevant.


Q.4. A ball is thrown vertically upward with a speed of 20 m/s. Draw a graph showing the velocity of the ball as a function of time as it goes up and then comes back.

HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1 | HC Verma Solutions - JEE


Q.5. The velocity of a particle is towards west at an instant. Its acceleration is not towards west, not towards east, not towards north and towards south. Give an example of this type of motion.

Motion of a projectile at the highest point of its path: Because at this point, the projectile has only horizontal component of velocity. So, it can have velocity towards west and acceleration in the vertically downward direction.


Q.6. At which point on its path a projectile has the smallest speed?

A projectile has the lowest speed at the highest point of its path because the vertical component of velocity is zero at this point.


Q.7. Two particles A and B start from rest and move for equal time on a straight line. The particle A has an acceleration a for the first half of the total time and 2a for the second half. The particle B has an acceleration 2a for the first and a for the second half. Which particle has covered larger distance?

HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1 | HC Verma Solutions - JEE
From the velocity–time graph, we have:
Distance covered by A = HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1 | HC Verma Solutions - JEE
Distance covered by B = HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1 | HC Verma Solutions - JEE
∴ Distance covered by A < Distance covered by B


Q.8. If a particle is accelerating, it is either speeding up or speeding down. Do you agree with this statement?

Acceleration does not mean speeding up or speeding down. It means the change of velocity either in direction or in magnitude.


Q.9. A food packet is dropped from a plane going at an altitude of 100 m. What is the path of the packet as seen from the plane? What is the path as seen from the ground ? If someone asks "what is the actual path", what will you answer?

The path of the packet (as seen from the plane) is a vertically downward straight line, as the horizontal velocity of the packet and the plane is the same.
As seen from the ground, the path of the packet is a parabola.
The path is defined with respect to some reference frame. As there is no absolute reference frame, no actual path is defined.


Q.10.1.  Give example where  the velocity of a particle is zero but its acceleration is not zero.

At the highest point when a particle is thrown vertically upwards.


Q.10.2. Give example where the velocity is opposite in direction to the acceleration.

While going up when a particle is thrown vertically upwards.


Q.10.3. Give example where the velocity is perpendicular to the acceleration.

 At the highest point of a full projectile.


Q.11. In figure shows the x coordinate of a particle as a function of time. Find the sings of vx and ax at t = t1, t = t2 and t = t3.
HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1 | HC Verma Solutions - JEE

Slope of the x–t graph gives the velocity and change in the slope gives the acceleration.
At t = t1,
Slope = Positive ⇒ Velocity = Positive
Slope is increasing ⇒ Acceleration = Positive
At t = t2,
Slope = Constant ⇒ Velocity = Zero
Slope is constant ⇒ Acceleration = Negative
At t = t3,
Slope = Negative ⇒ Velocity = Negative
Slope is increasing ⇒ Acceleration = Negative


Q.12. A player hits a baseball at some angle. The ball goes high up in space. The player runs and catches the ball before it hits the ground. Which of the two (the player or the ball) has greater displacement?

The displacement of the ball and the player is the same, as the initial and final points are the same.


Q.13. The increase in the speed of a car is proportional to the additional petrol put into the engine. Is it possible to accelerate a car without putting more petrol or less petrol into the engine?

Yes, it is possible to accelerate a car without putting more petrol or less petrol in the engine. This can be done by driving the car on a circular or curved track at a uniform speed.


Q.14. Rain is falling vertically. A man running on the road keeps his umbrella tilted but a man standing on the street keeps his umbrella vertical to protect himself from the rain. But both of them keep their umbrella vertical to avoid the vertical sun-rays. Explain.

The speed of rain is less, so as we run, the direction of the relative velocity of the rain changes. But as the speed of light is very high, there is a measurable change in the relative velocity of light w.r.t. a person due to the relative motion between the sunrays and the person.

Multiple Choice Questions

Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:A motor car is going due north at a speed of 50 km/h. It makes a 90° left turn without changing the speed. The change in the velocity of the car is about
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Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:In figure shows the displacement-time graph of a particle moving on the X-axis. 
HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1 | HC Verma Solutions - JEE
View Solution

Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:A particle has a velocity u towards east at t = 0. Its acceleration is towards west and is constant. Let xA and xB be the magnitude of displacements in the first 10 seconds and the next 10 seconds 
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Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:In the arrangement shown in figure the ends P and Q of an inextensible string move downwards with uniform speed u. Pulleys A and B are fixed. The mass M moves upwards with a speed 
HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1 | HC Verma Solutions - JEE
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Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:A person travelling on a straight line moves with a uniform velocity v1 for some time and with uniform velocity v2 for the next equal time. The average velocity v is given by
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Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:A person travelling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocity v2 for the next equal distance. The average velocity v is given by
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Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:A stone is released from an elevator going up with an acceleration a. The acceleration of the stone after the release is 
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Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:A person standing near the edge of the top of a building throws two balls A and B. the ball A is thrown vertically upward and B is thrown vertically downward with the same speed. The ball A hits the ground with a speed vA and the ball B this the ground with a speed vB. We have
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Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:In a projectile motion the velocity 
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Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:Two bullets are fired simultaneously, horizontally and with different speeds from the same place. Which bullet will hit he ground first?
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Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:The range of a projectile fired at an angle of 15° is 50 m. If it is fired with the same speed at an angle of 45°, its range will be 
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Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:Two projectiles A and B are projected with angle of projection 15° for the projectile A and 45° for the projectile B. If RA and RB be the horizontal range for the two projectiles, then
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Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:A river is flowing from west to east at a speed of 5 metres per minute. A man on the south bank of the river, capable of swimming at 10 metres per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction. 
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*Multiple options can be correct
Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:Consider the motion of the tip of the minute hand of a clock. In one hour
Check
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*Multiple options can be correct
Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:A particle moves along the X-axis as x = u (t − 2 s) + a (t − 2 s)2.
Check
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*Multiple options can be correct
Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:Pick the correct statements:
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*Multiple options can be correct
Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:An object may have
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*Multiple options can be correct
Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:Mark the correct statements for a particle going on a straight line:
Check
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*Multiple options can be correct
Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:The velocity of a particle is zero at t = 0.
Check
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Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:Mark the correct statements:
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*Multiple options can be correct
Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:The velocity-time plot for a particle moving on a straight line is shown in the figure. 
HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1 | HC Verma Solutions - JEE
Check
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Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:In figure shows the position of a particle moving on the X-axis as a function of time.
HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1 | HC Verma Solutions - JEE
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Question for HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1
Try yourself:The accelerations of a particle as seen from two frames S1 and S2 have equal magnitude 4 m/s2.
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FAQs on HC Verma Questions and Solutions: Chapter 3- Rest and Motion: Kinematics- 1 - HC Verma Solutions - JEE

1. What is kinematics?
Ans. Kinematics is the branch of physics that deals with the study of motion of objects without considering the cause of motion. It focuses on describing the position, velocity, and acceleration of objects without taking into account the forces acting on them.
2. How is rest defined in kinematics?
Ans. In kinematics, rest is defined as the state of an object when it is not changing its position with respect to its surroundings. An object at rest has zero velocity and zero acceleration.
3. What is the difference between average velocity and instantaneous velocity?
Ans. Average velocity is calculated by dividing the total displacement of an object by the total time taken. It gives the overall rate of change of position. On the other hand, instantaneous velocity is the velocity of an object at a particular instant of time. It is the limit of average velocity as the time interval approaches zero.
4. Can an object be in motion and still have zero velocity?
Ans. Yes, an object can be in motion and still have zero velocity. This can happen when the object is moving in a circular path. Although the object is continuously changing its direction, its displacement in one complete revolution is zero, resulting in zero average velocity.
5. What is the difference between speed and velocity?
Ans. Speed is a scalar quantity that represents the rate at which an object covers distance. It does not depend on direction and is always positive. On the other hand, velocity is a vector quantity that represents both the speed and direction of an object. It is the rate of change of displacement and can be positive or negative depending on the direction of motion.
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