In `S=a+bt+ct^2`. S is measured in metres and t in seconds. The unit of c is

Options

A. None
B. m
C. `ms^(-1)`
D. `ms^(-2)`

Explanation

To find the unit of \( c \) in the equation \( S = a + bt + ct^2 \), we can follow these steps:

### Step 1: Identify the units of each term in the equation
The equation consists of four terms: \( S \), \( a \), \( bt \), and \( ct^2 \). Since all terms in the equation must have the same dimensions, we will start by identifying the units of \( S \) and \( t \).

- The unit of \( S \) (displacement) is measured in **meters (m)**.
- The unit of \( t \) (time) is measured in **seconds (s)**.

### Step 2: Analyze the terms
1. **Term 1:** \( S \) has units of meters (m).
2. **Term 2:** \( a \) must also have units of meters (m) since it is added to \( S \).
3. **Term 3:** \( bt \) must also have units of meters (m). Since \( t \) is in seconds (s), we can express the units of \( b \) as follows:
\[ \text{Units of } b = \frac{\text{Units of } S}{\text{Units of } t} = \frac{\text{m}}{\text{s}} \quad \text{(units of } b \text{ is m/s)} \]

4. **Term 4:** \( ct^2 \) must also have units of meters (m). Since \( t^2 \) has units of seconds squared (s²), we can express the units of \( c \) as follows:
\[ \text{Units of } c = \frac{\text{Units of } S}{\text{Units of } t^2} = \frac{\text{m}}{\text{s}^2} \]

### Step 3: Finalize the unit of \( c \)
Thus, the unit of \( c \) can be expressed as:
\[ \text{Units of } c = \text{m} \cdot \text{s}^{-2} \]

### Conclusion
The unit of \( c \) is **meters per second squared (m/s²)**.