A brick becomes dislodged from the Empire State Building (at a height of 1175 feet) and falls to the sidewalk below. Write the position s(t), velocity v(t), and acceleration a(t) as functions of time.
A) $s ( t ) = 16 t ^ { 2 } + 1175$ ; $v ( t ) = 32 t$ ; $a ( t ) = 32$
B) $s ( t ) = - 16 t ^ { 2 } - 1175$ ; $v ( t ) = - 32 t$ ; $a ( t ) = - 32$
C) $s ( t ) = - 16 t ^ { 2 } + 1175$ ; $v ( t ) = - 32 t$ ; $a ( t ) = - 32$
D) $s ( t ) = 16 t ^ { 2 } - 1175$ ; $v ( t ) = - 32 t$ ; $a ( t ) = - 32$
E) $s ( t ) = - 16 t ^ { 2 } + 1175$ ; $v ( t ) = - 32$ ; $a ( t ) = - 32 t$

Question

Quizplus · Accepted Answer

The correct equations for the position, velocity, and acceleration of an object in free fall near the Earth's surface, with downward being the positive direction and starting from a height of 1175 feet, are $s(t) = -16t^2 + 1175$, $v(t) = -32t$, and $a(t) = -32$, respectively. This accounts for the acceleration due to gravity being $32 \text{ ft/s}^2$ downward, hence the negative signs in the equations.

A Brick Becomes Dislodged from the Empire State Building (At s(t)=16t2+1175s ( t ) = 16 t ^ { 2 } + 1175s(t)=16t2+1175

A Brick Becomes Dislodged from the Empire State Building (At $s ( t ) = 16 t ^ { 2 } + 1175$