$$ s=u t+\frac{1}{2} a t^{2} \quad $$ Solve for $$ u $$ given $$ s=20, t=2 $$ and $$ a=4 $$. +Workspace

Question

UpStudy AI · Accepted Answer

Certainly! Let's solve for $$ u $$ step by step using the given equation and values.

### Given:
- Equation: $$ s = u t + \frac{1}{2} a t^{2} $$
- $$ s = 20 $$ meters
- $$ t = 2 $$ seconds
- $$ a = 4 $$ meters/second²

### Step 1: Plug in the Known Values

Substitute the given values into the equation:

$$
20 = u \times 2 + \frac{1}{2} \times 4 \times (2)^2
$$

### Step 2: Simplify the Equation

First, calculate $$ \frac{1}{2} \times 4 \times (2)^2 $$:

$$
\frac{1}{2} \times 4 = 2
$$
$$
(2)^2 = 4
$$
$$
2 \times 4 = 8
$$

Now, the equation becomes:

$$
20 = 2u + 8
$$

### Step 3: Solve for $$ u $$

Subtract 8 from both sides to isolate the term with $$ u $$:

$$
20 - 8 = 2u
$$
$$
12 = 2u
$$

Divide both sides by 2 to solve for $$ u $$:

$$
u = \frac{12}{2} = 6
$$

### Conclusion

The initial velocity $$ u $$ is **6 meters/second**.
$$ u = 6 $$ meters/second

\( s=u t+\frac{1}{2} a t^{2} \quad \) Solve for \( u \) given \( s=20, t=2 \) and \( a=4 \). +Workspace