Gravity is an ever-present reminder that we live in a world of forces. When we throw a ball into the air, it doesn't sail off into space, but is accelerated back to earth. If we wanted to know where a falling object is at any time t, how fast it is moving, and how fast the velocity is changing, we can use these equations for the position, velocity, and acceleration:
x(t) = x(0) + v(0) + 1/2g * t2 (1)
The position at time t x(t) is the initial position x(0) plus initial velocity v(0) plus one half the gravitational constant g times time squared t2 .
v(t) = v(0) + g * t (2)
The velocity at time t v(t) is the initial velocity v(0) plus the gravitational constant g times time t.
a(t) = g (3)
The acceleration at time t a(t) is just the gravitational constant g.
Given that the gravitational constant g is 9.8 meters/second2, we can calculate the time it takes for an object to fall d meters. We start with
d = 0 + 0 + 1/2 * 9.8 * t2 from equation (1)
and solve for t, giving: t = sqrt(2d / 9.8) seconds (4)
Then we can determine the velocity with which the object will hit the ground by using (2) with the t from (4) to get v = 9.8 * t
Try different heights for the tower and ball in the simulation above, and note how the acceleration is demonstrated by the increasing distance between successive strobe images as the ball falls.
Subject Index for all interactive diagrams
interactagram.com - Physics - Kinamatics - Position, Velocity, and Acceleration - Falling Objects (Gravity)
Source Flash: fallingObjects.zip
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