Experiments show that, when air resistance can be ignored, all bodies fall
with the same acceleration. 

This acceleration is given the symbol g. 

The value of g on (or near) the surface of the earth is about 9.81ms^{2}. 



The acceleration due to gravity is not exactly the same at all
points on the earth’s surface. 

Small variations in g are due to 

1. 
altitude 
as you go higher you are moving away from the centre of mass of
the earth 
2. 
latitude 
the earth is not a perfect sphere so at different
latitudes you are at different distances from the centre of mass of
the earth 
3. 
the rotation of the earth 
The value of g is less than it would be if the earth
did not rotate. The value of g is reduced most at places where the
speed of circular motion is greatest, that is, on the
equator. 




A value for g at any point on the earth's surface can be
calculated using the following formula (from "Physical Constants", W.H.C. Childs) 



if you have a few minutes to spare! 

A quick look at the numbers in this formula tells us that, for moderate
altitudes, g does not change very much at different places. 



Velocity against Time Graphs for a Falling Body 




This graph shows what we would expect to happen if a body could be allowed
to fall freely, near the earth's surface, in a vacuum. 



With no air
resistance, there is only one force acting on the body, gravity, so the
slope of the graph would be constant at about 9.81ms^{2}. 






In practice, there is air resistance acting on falling bodies. 



The
slope of this graph starts out at 9.81ms^{2}
but gradually decreases as the body moves faster. 



After a
certain time (which depends on the shape of the body and the density of the
materials of which it is made) the body reaches a maximum speed called the
terminal speed (or terminal velocity), v_{t} 



At this
speed, the magnitude of the force due to air resistance, is equal to the
force of gravity. 



The fact that bodies reach a terminal speed when falling through air reminds
us that the force of air resistance increases with the speed of the body. 

This is true for other fluids. 

For example, a body falling through water gives a similar graph
though with much smaller terminal speed (for a given body). 



A person "skydiving" typically reaches speeds of 50 to 60ms^{1},
however it can be much faster. 
