Questions: Solve (S=a(x-v t)) for (t)

Transcript text: 3) Solve $S=a(x-v t)$ for $t$

Solution

Solution Steps

To solve the equation $ S = a(x - vt) $ for $ t $, we need to isolate $ t $ on one side of the equation. This involves a few algebraic steps: first, divide both sides by $ a $, then isolate $ vt $, and finally solve for $ t $.

Step 1: Divide Both Sides by $ a $

Given the equation $ S = a(x - vt) $, we start by dividing both sides by $ a $: \[ \frac{S}{a} = x - vt \]

Step 2: Isolate $ vt $

Next, we isolate the term involving $ t $ by subtracting $ x $ from both sides: \[ \frac{S}{a} - x = -vt \]

Step 3: Solve for $ t $

Finally, we solve for $ t $ by dividing both sides by $-v$: \[ t = \frac{\frac{S}{a} - x}{-v} \] Simplifying the expression, we get: \[ t = \frac{-S + ax}{av} \]

Final Answer

$\boxed{t = \frac{ax - S}{av}}$

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