Solve the following formula for $t$.
$S=\frac{1}{2}\left(V_0+V_1\right) t$
A. $t=\frac{S}{V_0+V_1}$
B. can't be solved for $t$
C. $t=\frac{V_0+V_1}{2 S}$
D. $t=\frac{2 S}{V_0+V_1}$
Answer (2)
Multiply both sides of the equation by 2: 2 S = ( V 0 + V 1 ) t .
Divide both sides by ( V 0 + V 1 ) to isolate t : t = V 0 + V 1 2 S .
The solution for t is t = V 0 + V 1 2 S .
The correct answer is D: t = V 0 + V 1 2 S
Explanation
Understanding the Problem We are given the formula S = 2 1 ( V 0 + V 1 ) t and we want to solve for t . This means we want to isolate t on one side of the equation.
Multiply by 2 First, let's multiply both sides of the equation by 2 to get rid of the fraction: 2 × S = 2 × 2 1 ( V 0 + V 1 ) t 2 S = ( V 0 + V 1 ) t
Divide to Isolate t Now, to isolate t , we need to divide both sides of the equation by ( V 0 + V 1 ) : V 0 + V 1 2 S = V 0 + V 1 ( V 0 + V 1 ) t t = V 0 + V 1 2 S
Final Answer Therefore, the solution for t is t = V 0 + V 1 2 S . Comparing this to the given options, we see that it matches option D.
Examples
In physics, this formula can be used to calculate the time it takes for an object to travel a certain distance S with a constant acceleration, given its initial velocity V 0 and final velocity V 1 . For example, if a car accelerates from 20 m/s to 30 m/s and travels 100 meters, we can use this formula to find the time it took to accelerate. Understanding how to rearrange formulas like this is crucial for solving many real-world problems in physics and engineering.
By multiplying the equation S = 2 1 ( V 0 + V 1 ) t by 2 and then dividing by ( V 0 + V 1 ) , we isolate t as t = V 0 + V 1 2 S . Therefore, the correct answer is option D.
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