Question

In left column, some statements related to various physical quantities are given while in Right column information about motion of a particle moving along a straight line are given. Match the entries of left column with the entries of right column.

Column 1	Column 2
Distance is always equal to magnitude of displacement	Initial velocity zero and constant acceleration
Velocity $=$average velocity over any interval	Direction of motion is not changing
Average speed and magnitude of velocity over same time interval are equal.	Acceleration is constant and no information about initial velocity
Velocity is continuously increasing.	Initial velocity and acceleration are in the same direction.

Answer 1

Part A:

1. The distance is always equal to the magnitude of displacement when a body moves in on a straight path
2. The distance is also always equal to the magnitude of displacement when the direction of velocity and acceleration of the body remains the same throughout the motion.
3. For a straight-line motion, the initial velocity of the body can be zero.
4. For a straight-line motion, the body can move with a constant acceleration i.e., the body can be accelerating.
5. Information about initial velocity is required because if the direction of initial velocity is not similar to the direction of acceleration the above case will not be true for all the conditions.

Thus, A - I, II, IV

Part B:

1. The velocity is equal to the average velocity over an interval if and only if the body is not accelerating and it is moving in a straight line.
2. For a body moving with a constant acceleration, the initial velocity can be zero and the final velocity will have a direction similar to the direction of the acceleration applied to it.
3. The direction of the motion of the body needs to be the same in order to keep the velocity equal to the average velocity over any interval.
4. Information about initial velocity is required because if the direction of initial velocity is not similar to the direction of acceleration the above case will not be true for all the conditions.

Thus, B - I, II, IV

Part C:

1. The average speed and magnitude of velocity over the same time interval are equal when the body is not accelerating and it is moving in a straight line without changing its direction of motion.
2. For a straight-line motion, the initial velocity of the body can be zero.
3. For a straight-line motion, the body can move with a constant acceleration i.e., the body can be accelerating.
4. Information about initial velocity is required because if the direction of initial velocity is not similar to the direction of acceleration the above case will not be true for all the conditions.

Thus, C - I, II, IV

Part D:

• The velocity increases continuously only when the body is accelerating with time in the same direction of velocity throughout the motion.
• The velocity can also increase continuously if the initial velocity is zero and the body is moving with a constant acceleration.
• Information about initial velocity is required because if the direction of initial velocity is not similar to the direction of acceleration the velocity can also decrease continuously.

Thus, D - I, II, IV

Hence, the correct answer is

Left column	Right column
Distance is always equal to the magnitude of displacement	Initial velocity is zero and constant acceleration, Direction of motion is not changing, Initial velocity and acceleration are in the same direction.
Velocity = average velocity over any interval	Initial velocity zero and constant acceleration, Direction of motion is not changing, Initial velocity and acceleration are in the same direction.
The average speed and magnitude of velocity over the same time interval are equal.	Initial velocity is zero and constant acceleration, Direction of motion is not changing, Initial velocity and acceleration are in the same direction.
Velocity is continuously increasing.	Initial velocity is zero and constant acceleration, Direction of motion is not changing, Initial velocity and acceleration are in the same direction.