The distance a free falling object has traveled can be modeled by the equation, `d=(1)/(2)at^(2)` where a is acceleration due to gravity and t is the amount of time the object has fallen. What is t in terms of a and d?

Options

A. `t=sqrt((da)/(2))`
B. `t=sqrt((2d)/(a))`
C. `t=((da)/(2))^(2)`
D. `t=((3d)/(a))^(2)`

Answer

To find \( t \) in terms of \( a \) and \( d \) from the equation \( d = \frac{1}{2} a t^2 \), we can follow these steps:

### Step-by-Step Solution:

1. **Start with the given equation**:
\[ d = \frac{1}{2} a t^2 \]

2. **Multiply both sides by 2** to eliminate the fraction:
\[ 2d = a t^2 \]

3. **Rearrange the equation** to isolate \( t^2 \):
\[ t^2 = \frac{2d}{a} \]

4. **Take the square root of both sides** to solve for \( t \):
\[ t = \sqrt{\frac{2d}{a}} \]

### Final Result:
Thus, \( t \) in terms of \( a \) and \( d \) is:
\[ t = \sqrt{\frac{2d}{a}} \]