Solve the following formula for $a$.
$s=V_0 t+\frac{1}{2} a t^2$
A. $a=\frac{2\left(s-V_0 t\right)}{t^2}$
B. $a=\frac{2\left(s+V_0 t\right)}{t^2}$
C. $a=\frac{t^2}{2\left(s-V_0 t\right)}$
D. $a=\frac{2\left(s+V_0 t\right)}{2 t}$
Answer (2)
Subtract V 0 t from both sides: s − V 0 t = 2 1 a t 2 .
Multiply both sides by 2: 2 ( s − V 0 t ) = a t 2 .
Divide both sides by t 2 : a = t 2 2 ( s − V 0 t ) .
The solution for a is a = t 2 2 ( s − V 0 t ) .
Explanation
Understanding the Problem We are given the equation s = V 0 t + 2 1 a t 2 and we want to solve for a . This means we want to isolate a on one side of the equation.
Isolating the term with 'a' First, subtract V 0 t from both sides of the equation to get: s − V 0 t = 2 1 a t 2
Eliminating the fraction Next, multiply both sides of the equation by 2 to eliminate the fraction: 2 ( s − V 0 t ) = a t 2
Isolating 'a' Finally, divide both sides of the equation by t 2 to isolate a : a = t 2 2 ( s − V 0 t )
Final Answer Therefore, the solution for a is: a = t 2 2 ( s − V 0 t ) This corresponds to option A.
Examples
This formula is used in physics to calculate the displacement of an object under constant acceleration. For example, if you know the initial velocity of a car ( V 0 ), the time it travels ( t ), and the distance it covers ( s ), you can use this formula to find the acceleration ( a ) of the car. This is useful in analyzing the motion of vehicles, projectiles, and other objects moving with constant acceleration.
The solution to the formula s = V 0 t + 2 1 a t 2 for a is a = t 2 2 ( s − V 0 t ) , which corresponds to option A.
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