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

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**.