In `S=ut+(1)/(2)at^(2)`, `S=96,t=8 and a=2`, find u.

Options

A. 2
B. 8
C. 4
D. 1

Explanation

To solve the equation \( S = ut + \frac{1}{2}at^2 \) for \( u \), we will follow these steps:

### Step 1: Write down the formula and substitute the known values.
The formula we are using is:
\[ S = ut + \frac{1}{2}at^2 \]
Given values are:
- \( S = 96 \)
- \( t = 8 \)
- \( a = 2 \)

Substituting these values into the formula:
\[ 96 = u(8) + \frac{1}{2}(2)(8^2) \]

### Step 2: Calculate \( \frac{1}{2}at^2 \).
First, we need to calculate \( \frac{1}{2}(2)(8^2) \):
\[ 8^2 = 64 \]
Now substituting this back:
\[ \frac{1}{2}(2)(64) = 1 \times 64 = 64 \]

### Step 3: Substitute this value back into the equation.
Now we can rewrite the equation:
\[ 96 = 8u + 64 \]

### Step 4: Isolate \( 8u \).
To isolate \( 8u \), subtract 64 from both sides:
\[ 96 - 64 = 8u \]
\[ 32 = 8u \]

### Step 5: Solve for \( u \).
Now, divide both sides by 8 to find \( u \):
\[ u = \frac{32}{8} = 4 \]

### Final Answer:
Thus, the value of \( u \) is:
\[ u = 4 \]

---