In basic mechanics, for an object in a state of rest, the state of motion is considered to correspond to what value of speed?

Introduction / Context:
This question checks your understanding of the fundamental concept of rest and motion in mechanics. In physics, rest and motion are defined relative to a chosen reference frame. An object may be at rest with respect to one observer and moving with respect to another. However, within a given frame, the definition of rest is precise and linked to the object's speed. Knowing this helps you interpret kinematics problems correctly.

Given Data / Assumptions:

• An object is said to be in a state of rest.
• We are asked about the value of speed in this state.
• Options mention increasing speed, decreasing speed, inverse speed and zero speed.
• We assume a fixed reference frame, such as the ground or a laboratory frame.

Concept / Approach:
Speed is the rate at which an object covers distance, defined as distance travelled per unit time. If an object is at rest relative to a chosen frame, its position does not change with time in that frame. This implies that the distance travelled is zero over any time interval, so its speed must be zero. Rest means absence of motion, and motion requires non zero speed. Terms like increasing or decreasing speed describe changes in motion, not a state of rest. Therefore, zero speed correctly represents the rest state.

Step-by-Step Solution:
Step 1: Recall that speed v is defined as v = distance / time. Step 2: If an object is at rest with respect to an observer, its distance from that observer does not change with time. Step 3: Because the distance travelled in any time interval is zero, the calculated speed v must also be zero. Step 4: Understand that increasing speed would imply acceleration, while decreasing speed implies deceleration, both of which describe moving objects. Step 5: Recognise that terms like inverse speed have no standard meaning in basic definitions of rest and motion. Step 6: Conclude that zero speed is the only option that correctly represents a state of rest.

Verification / Alternative check:
Consider a book lying on a table in a room. For a person standing in the room, the book is at rest because its position relative to the room does not change. If you measure the distance the book travels over 10 seconds, it will be zero, and its speed is zero. However, for an observer on the Sun, both the book and the room are moving due to the Earth rotation and revolution. This shows that rest is relative, but within the chosen frame of the room, the state of rest clearly corresponds to zero speed.

Why Other Options Are Wrong:
Increasing speed refers to a moving object whose speed is getting larger with time; such an object is not at rest. Decreasing speed describes an object that is slowing down but still moving until its speed reaches zero. Inverse speed has no clear definition in elementary mechanics and does not match the physical meaning of rest.

Common Pitfalls:
Some learners confuse the words rest and constant speed. An object can move with constant non zero speed, which is still motion, not rest. The key is to check whether the position changes with time. Only when the position is unchanged within a frame do we say the object is at rest, and in that case its speed is zero. Always link the concept of rest with zero speed and zero displacement in the chosen reference frame.

Final Answer:
For an object in a state of rest, the corresponding speed is Zero speed.