HC Verma Solutions: Kinematics- Rest and Motion | HC Verma Solutions - JEE PDF Download

Ques 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?
Ans: The concept of absolute motion is often considered meaningless in the context of relative motion. In this view, the two opposing perspectives on the movement of the Earth and the Sun can be seen as equivalent. Thus, both viewpoints—whether the Earth is stationary with the Sun moving around it, or the other way around—are equally valid or equally flawed.

Ques 2: When a particle moves with constant velocity, its average velocity, its instantaneous velocity and its speed are all equal. Comment on this statement.
Ans: Constant velocity implies that a particle maintains the same speed and direction at all points in its motion. Therefore, both its average velocity and its instantaneous velocity will be equal. Since speed is a scalar quantity, it is equal in magnitude but does not have a direction.

Ques 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.
Ans: No, the velocities of the two cars are not equal. This is because the directions of the cars are different: one travels due north while the other moves due east. Velocity is a vector quantity, which means it has both magnitude and direction. As such, we cannot compare their velocities solely based on speed. Therefore, the question of which velocity is greater is irrelevant since they cannot be compared directly.

Ques 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.
Ans: 


Ques 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.
Ans: The motion of a projectile at the highest point of its path serves as a perfect example. At this stage, the projectile possesses only a horizontal component of velocity, which can be directed towards the west. Meanwhile, its acceleration is directed vertically downwards.

Ques 6: At which point on its path a projectile has the smallest speed?
Ans: A projectile has the lowest speed at the highest point of its path. This occurs because the vertical component of its velocity is zero at this point.

Ques 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?
Ans: 

From the velocity–time graph, we have:
Distance covered by
Distance covered by 
∴ Distance covered by A < Distance covered by B

Ques 8: If a particle is accelerating, it is either speeding up or speeding down. Do you agree with this statement?
Ans: Acceleration does not merely imply that an object is speeding up or slowing down. Instead, it refers to the change in velocity, which can occur in either direction or in magnitude. To elaborate:

• Acceleration can result from an increase in speed.
• It can also occur when an object decreases its speed.
• Furthermore, acceleration can happen without a change in speed, such as when an object changes direction.

Ques 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?
Ans: The path of the packet, as seen from the plane, is a vertically downward straight line. This is because the horizontal velocity of the packet is the same as that of the plane. Conversely, from the ground, the path of the packet appears as a parabola. The path is defined with respect to a reference frame. Since there is no absolute reference frame in physics, there is no fixed "actual path" that can be defined.

Ques 10: Give examples where (a) the velocity of a particle is zero but its acceleration is not zero, (b) the velocity is opposite in direction to the acceleration, (c) the velocity is perpendicular to the acceleration.
Ans: Examples of Particle Motion:

• (a) The velocity of a particle is zero but its acceleration is not zero at the highest point when a particle is thrown vertically upwards.
• (b) The velocity is opposite in direction to the acceleration while a particle is going upwards after being thrown vertically upwards.
• (c) The velocity is perpendicular to the acceleration at the highest point of a full projectile motion.