In `s=ut+(1)/(2)at^(2)`, if `s=16m,t=2` seconds and `a=5m//s^(2)`, then find the value of u by making u as the subject.

Options

A. 3m/s
B. 5m/s
C. 2m/s
D. 4m/s

Explanation

To find the value of \( u \) from the equation \( s = ut + \frac{1}{2}at^2 \), we will follow these steps:

### Step 1: Write down the given values
We have:
- \( s = 16 \) m
- \( t = 2 \) seconds
- \( a = 5 \) m/s²

### Step 2: Substitute the known values into the equation
The equation is:
\[ s = ut + \frac{1}{2}at^2 \]
Substituting the known values:
\[ 16 = u(2) + \frac{1}{2}(5)(2^2) \]

### Step 3: Calculate \( \frac{1}{2}at^2 \)
First, calculate \( 2^2 \):
\[ 2^2 = 4 \]
Now substitute this back into the equation:
\[ \frac{1}{2}(5)(4) = \frac{20}{2} = 10 \]

### Step 4: Substitute back into the equation
Now the equation becomes:
\[ 16 = 2u + 10 \]

### Step 5: Isolate \( 2u \)
Subtract 10 from both sides:
\[ 16 - 10 = 2u \]
\[ 6 = 2u \]

### Step 6: Solve for \( u \)
Now divide both sides by 2:
\[ u = \frac{6}{2} = 3 \]

### Step 7: State the final answer
Thus, the value of \( u \) is:
\[ u = 3 \text{ m/s} \]