Final answer:
To find the acceleration due to gravity from the formula d = v°t + 1/2at², set the initial velocity to zero and rearrange to a = 2d/t². For Earth, the value of g is approximately 9.8 m/s².
Step-by-step explanation:
To solve the formula d = v°t + 1/2at² for the acceleration due to gravity, we need to isolate a. Assuming the initial velocity (v°) is zero and we are just considering the free-fall motion, the equation reduces to d = 1/2at². We can then rearrange the equation to solve for acceleration, which gives a = 2d/t².
The acceleration due to gravity, g, is a special case of acceleration where we use a specific value for a. On Earth, this value is approximately g = 9.8 m/s². However, we are often interested in solving for acceleration in various other scenarios, and this rearranged formula allows us to do that.
In summary, acceleration is given by a = 2d/t², and when considering gravitational acceleration, it is g = -9.8 m/s² or g = 9.8 m/s², depending on the direction we take as positive in our coordinate system.