The velocity of a particle at an instant is `10 m s^(-1)`. After 3 s its velocity will becomes `16 m s^(-1)`. The velocity at 2 s, before the given instant will be

Options

A. `6 m s^(-1)`
B. `4 m s^(-1)`
C. `2 m s^(-1)`
D. `1 m s^(-1)`

Explanation

To find the velocity of the particle at 2 seconds before the given instant, we can follow these steps:

### Step 1: Identify the given values
- Initial velocity (u) at the given instant (t = 0): \( u = 10 \, \text{m/s} \)
- Final velocity (v) after 3 seconds: \( v = 16 \, \text{m/s} \)
- Time interval (t): \( t = 3 \, \text{s} \)

### Step 2: Calculate the acceleration
Using the formula for acceleration:
\[ a = \frac{v - u}{t} \]
Substituting the known values:
\[ a = \frac{16 \, \text{m/s} - 10 \, \text{m/s}}{3 \, \text{s}} = \frac{6 \, \text{m/s}}{3 \, \text{s}} = 2 \, \text{m/s}^2 \]

### Step 3: Find the velocity at \( t = -2 \, \text{s} \) (2 seconds before the given instant)
We need to find the initial velocity (u') at \( t = -2 \, \text{s} \). We can use the kinematic equation:
\[ v = u + at \]
Rearranging the equation to find \( u' \):
\[ u' = v - at \]
At \( t = 2 \, \text{s} \) before the given instant, the time interval for acceleration will be:
\[ t = 2 \, \text{s} \]
Substituting the values:
\[ u' = 10 \, \text{m/s} - (2 \, \text{m/s}^2 \times 2 \, \text{s}) = 10 \, \text{m/s} - 4 \, \text{m/s} = 6 \, \text{m/s} \]

### Conclusion
The velocity of the particle at 2 seconds before the given instant is \( 6 \, \text{m/s} \).

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