An object falling in a vacuum near the surface of the earth experiences a gravitational force in the z direction given by

F_z = −mg,

where g is called the acceleration due to gravity and is equal to 9.80 m s⁻². This corresponds to a constant acceleration

a_z = −g.

Find the expression for the position of the particle as a function of time. Find the position of the particle at time t = 1.00 s if its initial position is z = 10.00 m and its initial velocity is v_z = 0.