STATEMENT - 1 : Equation of motion `(v=u+at)` is applicable even if the acceleration is non-uniform.
STATEMENT - 2 : The initial velocity of a body is u and its acceleration is ft where f is a constant and t is time.
The displacement in time t is `(ut+(1)/(2)ft^(2))`.
STATEMENT - 3 : The area enclosed by the a-t graph and time axis gives the change in velocity of the body.

Options

A. FFT
B. TTF
C. TTF
D. FTT

Answer

To solve the given question, we will analyze each statement one by one and determine their validity.

### Step 1: Analyze Statement 1
**Statement 1:** "Equation of motion \( v = u + at \) is applicable even if the acceleration is non-uniform."

- The equation \( v = u + at \) is derived under the assumption of uniform acceleration. This means that the acceleration \( a \) is constant throughout the motion. If the acceleration is non-uniform, this equation does not hold true because the acceleration changes over time. Therefore, Statement 1 is **false**.

### Step 2: Analyze Statement 2
**Statement 2:** "The initial velocity of a body is \( u \) and its acceleration is \( ft \) where \( f \) is a constant and \( t \) is time. The displacement in time \( t \) is \( ut + \frac{1}{2} ft^2 \)."

- Here, the acceleration is given as \( a = ft \), which is not constant but varies with time. The correct expression for displacement when acceleration is not constant requires integration. The displacement \( s \) can be calculated using the formula:
\[ s = ut + \int_0^t (ft) dt \]
Integrating \( ft \) from \( 0 \) to \( t \) gives:
\[ s = ut + \frac{1}{2} f t^2 \]
However, since \( f \) is treated as a constant in this context, the statement is misleading. The displacement formula provided is correct only if \( a \) is constant. Therefore, Statement 2 is also **false**.

### Step 3: Analyze Statement 3
**Statement 3:** "The area enclosed by the a-t graph and time axis gives the change in velocity of the body."

- The area under the acceleration-time graph (a-t graph) represents the change in velocity. This is because acceleration is defined as the rate of change of velocity. Mathematically, this can be expressed as:
\[ \Delta v = \int a \, dt \]
Thus, the area under the a-t graph indeed gives the change in velocity. Therefore, Statement 3 is **true**.

### Conclusion
Based on the analysis:
- Statement 1 is **false**.
- Statement 2 is **false**.
- Statement 3 is **true**.

Thus, the correct answer is that only Statement 3 is true.