66.4k views
1 vote
In physics, the following formula relates your distance above the ground, (d), relative to how long, (t), an object has been in the air: d = v°t + 1/2at²

Solve for the formula for a, the acceleration due to gravity.

1 Answer

2 votes

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 () 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.

User Alex Guerra
by
8.0k points