A particle goes from A to B in 10s with uniform acceleration. Its velocity at A and B are 5 m/s and 25 m/s. Its acceleration (in `m//s^(2)`) is

Options

A. 0.5
B. 2.5
C. 2
D. 3

Answer

To solve the problem step by step, we will use the equations of motion under uniform acceleration.

### Given Data:
- Initial velocity, \( u = 5 \, \text{m/s} \)
- Final velocity, \( v = 25 \, \text{m/s} \)
- Time taken, \( t = 10 \, \text{s} \)

### Step 1: Use the equation of motion
We will use the first equation of motion, which relates initial velocity, final velocity, acceleration, and time:
\[ v = u + at \]

### Step 2: Substitute the known values
Substituting the known values into the equation:
\[ 25 = 5 + a \cdot 10 \]

### Step 3: Rearrange the equation to solve for acceleration \( a \)
First, we will isolate \( a \):
\[ 25 - 5 = a \cdot 10 \]
\[ 20 = a \cdot 10 \]

### Step 4: Solve for \( a \)
Now, divide both sides by 10:
\[ a = \frac{20}{10} = 2 \, \text{m/s}^2 \]

### Conclusion
The acceleration of the particle is \( 2 \, \text{m/s}^2 \).