A coin is dropped from the Leaning Tower of Pisa. It starts from rest and falls freely. Neglecting air resistance, compute the coin's position and velocity at 1.0 s, 2.0 s and 3.0 s.

the distance fallen at time t seconds is

4.9 t^2 meters

I leave it up to you to discover how high the tower is, and just what you mean by "position."

To compute the coin's position and velocity at different times, we need to use the equations of motion for freely falling objects.

The first equation we will use is the equation for displacement:

d = v₀t + 0.5at²

where d is the displacement (position), v₀ is the initial velocity (which is zero in this case because the coin starts from rest), t is the time, and a is the acceleration due to gravity.

The second equation is the equation for velocity:

v = v₀ + at

where v is the final velocity, v₀ is the initial velocity, t is the time, and a is the acceleration due to gravity.

In this case, the coin is in free fall, so the acceleration due to gravity, a, is approximately 9.8 m/s².

Now let's compute the coin's position and velocity at 1.0 s, 2.0 s, and 3.0 s.

At 1.0 s:
- Position (displacement):
d = (0 m/s)(1.0 s) + 0.5(9.8 m/s²)(1.0 s)² = 4.9 m
- Velocity:
v = (0 m/s) + (9.8 m/s²)(1.0 s) = 9.8 m/s

At 2.0 s:
- Position (displacement):
d = (0 m/s)(2.0 s) + 0.5(9.8 m/s²)(2.0 s)² = 19.6 m
- Velocity:
v = (0 m/s) + (9.8 m/s²)(2.0 s) = 19.6 m/s

At 3.0 s:
- Position (displacement):
d = (0 m/s)(3.0 s) + 0.5(9.8 m/s²)(3.0 s)² = 44.1 m
- Velocity:
v = (0 m/s) + (9.8 m/s²)(3.0 s) = 29.4 m/s

Therefore, at 1.0 s, the coin's position is 4.9 m and its velocity is 9.8 m/s. At 2.0 s, the coin's position is 19.6 m and its velocity is 19.6 m/s. At 3.0 s, the coin's position is 44.1 m and its velocity is 29.4 m/s.