An object falls freely in a straight line and experiences air resistance proportional to its? speed; this means its acceleration is ? a(t)=? ? kv(t), where k is a positive constant and v is the? object's velocity. the speed of the object decreases from 800 ft/s to 700ft/s over a distance of 1400 ft. approximate the time required for this deceleration to occur?

t = 1.068 s

Step-by-step explanation:

given,

a(t) =- k v(t)

speed of the object decreases from 800 ft/s to 700 ft/s

distance = 1400 ft

time for deceleration = ?

a(t) =- k v(t)

integrating both side

..........(1)

since,

from equation 1

putting value of k in equation (1)

t = 1.068 s

answer: all the values are within because it has a pattern that repeats from -6 to 4.

good luck!