Question

A brick becomes dislodged from the top of the Empire State Building (at a height of 1250 feet) and falls to the sidewalk below. What is the position formula, velocity, and acceleration functions of the brick?

Answer 1

The position formula for a falling object is y(t) = y0 + v0t + 0.5at^2. The velocity function is v(t) = v0 + at, and the acceleration function is a(t) = -9.8 m/s^2.

Step-by-step explanation:

The position formula for a falling object is given by the equation:

y(t) = y0 + v0t + 0.5at2

where:

• y(t) is the position of the object at time t
• y0 is the initial position of the object
• v0 is the initial velocity of the object
• a is the acceleration due to gravity (approximately -9.8 m/s2)
• t is the time

The velocity function is given by:

v(t) = v0 + at

And the acceleration function is simply the constant acceleration due to gravity:

a(t) = -9.8 m/s2