How Do You Calculate Acceleration and Distance of a Free-Falling Object?

[jsm6252]

my question leads to something bigger but to start g force on Earth is 9.8m/s2 for simlicity let's say 10.

1-is it rite to say if you drop an object in the 1st sec its acceleration is 10m/s2 in the 2nd sec it's 100m/s then in the 3rd sec it's 10000 m/s
2-if the above is correct what is the distance traveled i.e in the 3rd sec has the object traveled a total of 10000m.
3-how do you calculate g 100km above the earth.

 

[jtbell]

1-is it rite to say if you drop an object in the 1st sec its acceleration is 10m/s2 in the 2nd sec it's 100m/s then in the 3rd sec it's 10000 m/s

No. After one second, its velocity is 10 m/s, after two seconds its velocity is 20 m/s, after three seconds its velocity is 30 m/s, etc. Its acceleration remains constant at 10 m/s^2.

 

[JaredJames]

To calculate g at 100km you need to use the equation:

g = (G*m₁*m₂) / r²

Where G is the gravitational constant, m₁ is the mass of the earth, m₂ is the mass of the body currently at 100km, r² is the distance from the centre of the Earth (Earth's radius plus altitude of 100km).

 

[jsm6252]

thank you

 

[SteamKing]

A quicker way to calculate g at a given altitude h is to use the relation:

g at h = g at sea level * (r Earth / (r Earth + altitude))^2

where r Earth = average radius of the earth.

The quantity G * m1 * m2 / r^2 is the gravitational force acting between two masses m1 and m2 which are a distance r apart.