The velocity of a block of mass `2kg` moving along `x-` axis at any time `t` is givne by `v=20-10t(m//s)` where `t` is in seconds and `v` is in `m//s`. At time `t=0`, the block is moving in positive `x-` direction.
The power due to net force on force on block at `t=3 sec. `is `:`

Options

A. `100` watts
B. 200 watts
C. 300 watts
D. 400 watts

Explanation

To solve the problem, we need to find the power due to the net force acting on a block of mass 2 kg at time \( t = 3 \) seconds. The velocity of the block is given by the equation \( v = 20 - 10t \) m/s.

### Step-by-step Solution:

1. **Calculate the velocity at \( t = 3 \) seconds:**
\[ v = 20 - 10t \]
Substituting \( t = 3 \):
\[ v = 20 - 10 \times 3 = 20 - 30 = -10 \text{ m/s} \]
The velocity of the block at \( t = 3 \) seconds is \( -10 \) m/s, indicating it is moving in the negative x-direction.

2. **Calculate the acceleration:**
The acceleration \( a \) can be found by differentiating the velocity function with respect to time:
\[ a = \frac{dv}{dt} = \frac{d}{dt}(20 - 10t) = -10 \text{ m/s}^2 \]

3. **Calculate the net force acting on the block:**
Using Newton's second law, \( F = ma \):
\[ F = m \cdot a = 2 \text{ kg} \cdot (-10 \text{ m/s}^2) = -20 \text{ N} \]
The net force acting on the block is \( -20 \) N, indicating it is directed in the negative x-direction.

4. **Calculate the power:**
Power \( P \) is given by the formula:
\[ P = F \cdot v \]
Substituting the values of force and velocity at \( t = 3 \):
\[ P = (-20 \text{ N}) \cdot (-10 \text{ m/s}) = 200 \text{ W} \]

### Final Answer:
The power due to the net force on the block at \( t = 3 \) seconds is **200 Watts**.