Starting from rest, the acceleration of a particle is `a=2(t-1)`. The velocity (i.e.`v=int" a dt "`) of the particle at t=10 s is :-

Options

A. 15 m/s
B. 25 m/s
C. 5 m/s
D. 80 m/s

Answer

To solve the problem, we need to determine the velocity of a particle at \( t = 10 \) seconds given its acceleration \( a = 2(t - 1) \) and that it starts from rest.

### Step-by-Step Solution:

1. **Understand the given acceleration**:
The acceleration of the particle is given by:
\[ a = 2(t - 1) \]

2. **Set up the integral for velocity**:
Since the particle starts from rest, we can find the velocity by integrating the acceleration with respect to time. The velocity \( v \) can be expressed as:
\[ v(t) = \int a \, dt = \int 2(t - 1) \, dt \]

3. **Perform the integration**:
We will integrate \( 2(t - 1) \):
\[ v(t) = \int 2(t - 1) \, dt = 2 \left( \frac{t^2}{2} - t \right) + C = t^2 - 2t + C \]
Here, \( C \) is the constant of integration.

4. **Determine the constant of integration**:
Since the particle starts from rest at \( t = 0 \), we have:
\[ v(0) = 0 \implies 0^2 - 2(0) + C = 0 \implies C = 0 \]
Thus, the expression for velocity simplifies to:
\[ v(t) = t^2 - 2t \]

5. **Calculate the velocity at \( t = 10 \) seconds**:
Now we substitute \( t = 10 \) into the velocity equation:
\[ v(10) = 10^2 - 2(10) = 100 - 20 = 80 \, \text{m/s} \]

### Final Answer:
The velocity of the particle at \( t = 10 \) seconds is:
\[ \boxed{80 \, \text{m/s}} \]