The velocity of a body moving with a uniform acceleration of `2m//sec^(2)` is `10m//sec`. Its velocity after an interval of 4sec is

Options

A. `12 m//sec`
B. `14m//sec`
C. `16m//sec`
D. `18m//sec`

Answer

To find the final velocity of a body moving with uniform acceleration, we can use the following kinematic equation:

\[ v = u + at \]

Where:
- \( v \) = final velocity
- \( u \) = initial velocity
- \( a \) = acceleration
- \( t \) = time

Given:
- Initial velocity, \( u = 10 \, \text{m/s} \)
- Acceleration, \( a = 2 \, \text{m/s}^2 \)
- Time interval, \( t = 4 \, \text{s} \)

### Step 1: Substitute the known values into the equation

We will substitute the values of \( u \), \( a \), and \( t \) into the equation:

\[ v = 10 \, \text{m/s} + (2 \, \text{m/s}^2 \times 4 \, \text{s}) \]

### Step 2: Calculate the product of acceleration and time

Now, we calculate \( 2 \, \text{m/s}^2 \times 4 \, \text{s} \):

\[ 2 \, \text{m/s}^2 \times 4 \, \text{s} = 8 \, \text{m/s} \]

### Step 3: Add the initial velocity to the product

Now, we add this result to the initial velocity:

\[ v = 10 \, \text{m/s} + 8 \, \text{m/s} \]

### Step 4: Calculate the final velocity

Finally, we calculate:

\[ v = 18 \, \text{m/s} \]

Thus, the final velocity of the body after an interval of 4 seconds is **18 m/s**.

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