If `y` is displacement and `t` is time, unit of `(d^(2)y)/(dt^(2))` will be

Options

A. `(m^(2))/(sec^(2))`
B. `(m)/(sec)`
C. `(m^(2))/(sec)`
D. `(m)/(sec^(2))`

Answer

To find the unit of \(\frac{d^2y}{dt^2}\), we can follow these steps:

### Step 1: Understand the variables
- Let \(y\) represent displacement, which is measured in meters (m).
- Let \(t\) represent time, which is measured in seconds (s).

### Step 2: Find the first derivative \(\frac{dy}{dt}\)
- The first derivative \(\frac{dy}{dt}\) represents the rate of change of displacement with respect to time, which is velocity.
- The unit of velocity is meters per second (m/s).

### Step 3: Find the second derivative \(\frac{d^2y}{dt^2}\)
- The second derivative \(\frac{d^2y}{dt^2}\) represents the rate of change of velocity with respect to time, which is acceleration.
- To find the unit of acceleration, we take the unit of velocity (m/s) and divide it by the unit of time (s).

### Step 4: Calculate the unit of \(\frac{d^2y}{dt^2}\)
- The unit of acceleration is given by:
\[ \text{Unit of } \frac{d^2y}{dt^2} = \frac{\text{Unit of velocity}}{\text{Unit of time}} = \frac{\text{m/s}}{\text{s}} = \text{m/s}^2 \]

### Conclusion
- Therefore, the unit of \(\frac{d^2y}{dt^2}\) is \(\text{m/s}^2\).

### Final Answer
- The unit of \(\frac{d^2y}{dt^2}\) is \(\text{m/s}^2\).

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