The position of an object moving in a straight line with constant acceleration can be expressed as x=x0+v0t+12at2, where x0 is the object's initial position, v0 is its initial velocity, a is its acceleration, and t is its time in motion.Which shows the equation solved for the acceleration of the object, a?
Question
The position of an object moving in a straight line with constant acceleration can be expressed as x=x0+v0t+12at2, where x0 is the object's initial position, v0 is its initial velocity, a is its acceleration, and t is its time in motion.Which shows the equation solved for the acceleration of the object, a?
Solution
To solve the equation for acceleration (a), we need to isolate 'a' on one side of the equation. Here are the steps:
- Start with the original equation: x = x0 + v0t + 1/2a*t^2
- Subtract x0 and v0t from both sides to isolate the term with 'a': x - x0 - v0t = 1/2at^2
- Multiply both sides by 2 to get rid of the fraction: 2*(x - x0 - v0t) = at^2
- Finally, divide both sides by t^2 to solve for 'a': a = 2*(x - x0 - v0*t) / t^2
So, the equation solved for the acceleration of the object, a, is a = 2*(x - x0 - v0*t) / t^2.
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