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If x=x(o)+(1)/(2)(v+v(o))t, what is v in...

If `x=x_(o)+(1)/(2)(v+v_(o))t`, what is v in terms of the other variables?

A

`(2(x-x_(o)))/(v_(o)t)`

B

`(2(x-x_(o)))/(t)-v_(o)`

C

`(t(x-x_(o)))/(2v_(o))`

D

`v_(o)t-(2(x-x_(o)))/(t)`

Text Solution

AI Generated Solution

The correct Answer is:
To isolate \( v \) in the equation \( x = x_0 + \frac{1}{2}(v + v_0)t \), we will follow these steps: 1. **Start with the original equation**: \[ x = x_0 + \frac{1}{2}(v + v_0)t \] 2. **Subtract \( x_0 \) from both sides**: \[ x - x_0 = \frac{1}{2}(v + v_0)t \] 3. **Multiply both sides by 2 to eliminate the fraction**: \[ 2(x - x_0) = (v + v_0)t \] 4. **Divide both sides by \( t \)** (assuming \( t \neq 0 \)): \[ \frac{2(x - x_0)}{t} = v + v_0 \] 5. **Subtract \( v_0 \) from both sides to isolate \( v \)**: \[ v = \frac{2(x - x_0)}{t} - v_0 \] Now we have \( v \) expressed in terms of the other variables. ### Final Result: \[ v = \frac{2(x - x_0)}{t} - v_0 \]
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