The speed after time t can be expressed by the equation v_f = 9.81t.

The distance of the rocket after time t is d = 4.905t².

 Explanation

Using kinematic equation to find the final velocity given the acceleration and initial velocity:

 

v_f = v_o + at

 

where:

 

v_f = final velocity (m/s)

v_o = initial velocity (m/s)

a = acceleration (m/s²)

t = time (s)

 

The rocket starts from rest so that v_o = 0 m/s. And since this is a case of a free fall, we will be using a = +9.81 m/s². Therefore, the speed after time t is:

 

v_f = v_o + at

v_f = 0 + 9.81t

v_f = 9.81t

 

Another kinematic equation that we can use to find the distance after time t is:

 

d = v_ot + 0.5at²

 

^where:

d = distance (m)

v_o = initial speed (m/s)

t = time (s)

a = acceleration (m/s²)

 

Using again a = +9.81 m/s² as the acceleration and v_o = 0 m/s, the equation to find the distance of the rocket after time t is:

 

d = v_ot + 0.5at²

d = 0t + 0.5(9.81)t²

d = 4.905t²