The rate of change of displacement with time is

Options

A. speed
B. accerelation
C. retardation
D. velocity

Explanation

To solve the question "The rate of change of displacement with time is," we need to define the terms involved and derive the answer step by step.

### Step 1: Understand the concept of displacement
Displacement is defined as the shortest distance from the initial position to the final position of an object. It is a vector quantity, which means it has both magnitude and direction.

**Hint:** Remember that displacement is not the same as distance; it considers only the shortest path between two points.

### Step 2: Define the rate of change
The rate of change of any quantity with respect to time is defined as how much that quantity changes over a specific period. In this case, we are interested in how displacement changes over time.

**Hint:** Think about how we measure changes in quantities over time, like speed or velocity.

### Step 3: Relate displacement to time
The rate of change of displacement with respect to time can be expressed mathematically as:
\[ \text{Rate of change of displacement} = \frac{\text{Displacement}}{\text{Time}} = \frac{\Delta s}{\Delta t} \]
where \(\Delta s\) is the change in displacement and \(\Delta t\) is the change in time.

**Hint:** This formula is similar to how we calculate speed or velocity.

### Step 4: Define the term "velocity"
When we calculate the rate of change of displacement with time, we are actually defining the concept of velocity. Therefore, we can conclude that:
\[ \text{Velocity} = \frac{\Delta s}{\Delta t} \]

**Hint:** Remember that velocity is a vector quantity, which means it has both magnitude (how fast) and direction (where to).

### Final Answer:
The rate of change of displacement with time is called **velocity**.

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