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Python 3, 167 166 bytes

import time,random
t=time.time
p,s=input(),t()
while t()-s<len(p):print(p[:int(t()-s)]+''.join(chr(random.randint(32,126))for _ in range(len(p)-int(t()-s))))
print(p)
import time,random
t=time.time
p,s=input(),t()
while t()-s<len(p):print(p[:int(t()-s)]+''.join(chr(random.randint(32,126))for _ in range(len(p)-int(t()-s))))
print(p)

Reads input from stdin. A 171-byte version runs under Python 2 (replaced input with raw_input):

import time,random
t=time.time
p,s=raw_input(),t()
while t()-s<len(p):print(p[:int(t()-s)]+''.join(chr(random.randint(32,126))for _ in range(len(p)-int(t()-s))))
print(p)
import time,random
t=time.time
p,s=raw_input(),t()
while t()-s<len(p):print(p[:int(t()-s)]+''.join(chr(random.randint(32,126))for _ in range(len(p)-int(t()-s))))
print(p)

Ungolfed:

import random
import time

p = input()
start = time.time()
while time.time() - start < len(p): 
    print(
        p[:int(time.time() - start)] + 
        ''.join(chr(random.randint(32, 126)) for _ in range(len(p) - int(time.time()-start)))
    )
print(p)
import random
import time

p = input()
start = time.time()
while time.time() - start < len(p): 
    print(
        p[:int(time.time() - start)] + 
        ''.join(chr(random.randint(32, 126)) for _ in range(len(p) - int(time.time()-start)))
    )
print(p)

Python 3, 167 166 bytes

import time,random
t=time.time
p,s=input(),t()
while t()-s<len(p):print(p[:int(t()-s)]+''.join(chr(random.randint(32,126))for _ in range(len(p)-int(t()-s))))
print(p)

Reads input from stdin. A 171-byte version runs under Python 2 (replaced input with raw_input):

import time,random
t=time.time
p,s=raw_input(),t()
while t()-s<len(p):print(p[:int(t()-s)]+''.join(chr(random.randint(32,126))for _ in range(len(p)-int(t()-s))))
print(p)

Ungolfed:

import random
import time

p = input()
start = time.time()
while time.time() - start < len(p): 
    print(
        p[:int(time.time() - start)] + 
        ''.join(chr(random.randint(32, 126)) for _ in range(len(p) - int(time.time()-start)))
    )
print(p)

Python 3, 167 166 bytes

import time,random
t=time.time
p,s=input(),t()
while t()-s<len(p):print(p[:int(t()-s)]+''.join(chr(random.randint(32,126))for _ in range(len(p)-int(t()-s))))
print(p)

Reads input from stdin. A 171-byte version runs under Python 2 (replaced input with raw_input):

import time,random
t=time.time
p,s=raw_input(),t()
while t()-s<len(p):print(p[:int(t()-s)]+''.join(chr(random.randint(32,126))for _ in range(len(p)-int(t()-s))))
print(p)

Ungolfed:

import random
import time

p = input()
start = time.time()
while time.time() - start < len(p): 
    print(
        p[:int(time.time() - start)] + 
        ''.join(chr(random.randint(32, 126)) for _ in range(len(p) - int(time.time()-start)))
    )
print(p)
trimmed off a space
Source Link

Python 3, 167167 166 bytes

import time,random
t=time.time
p,s=input(),t()
while t()-s<len(p):print(p[:int(t()-s)]+''.join(chr(random.randint(32,126)) for _ in range(len(p)-int(t()-s))))
print(p)

Reads input from stdin. A 171-byte version runs under Python 2 (replaced input with raw_input):

import time,random
t=time.time
p,s=raw_input(),t()
while t()-s<len(p):print(p[:int(t()-s)]+''.join(chr(random.randint(32,126)) for _ in range(len(p)-int(t()-s))))
print(p)

Ungolfed:

import random
import time

p = input()
start = time.time()
while time.time() - start < len(p): 
    print(
        p[:int(time.time() - start)] + 
        ''.join(chr(random.randint(32, 126)) for _ in range(len(p) - int(time.time()-start)))
    )
print(p)

Python 3, 167 bytes

import time,random
t=time.time
p,s=input(),t()
while t()-s<len(p):print(p[:int(t()-s)]+''.join(chr(random.randint(32,126)) for _ in range(len(p)-int(t()-s))))
print(p)

Reads input from stdin. A 171-byte version runs under Python 2 (replaced input with raw_input):

import time,random
t=time.time
p,s=raw_input(),t()
while t()-s<len(p):print(p[:int(t()-s)]+''.join(chr(random.randint(32,126)) for _ in range(len(p)-int(t()-s))))
print(p)

Ungolfed:

import random
import time

p = input()
start = time.time()
while time.time() - start < len(p): 
    print(
        p[:int(time.time() - start)] + 
        ''.join(chr(random.randint(32, 126)) for _ in range(len(p) - int(time.time()-start)))
    )
print(p)

Python 3, 167 166 bytes

import time,random
t=time.time
p,s=input(),t()
while t()-s<len(p):print(p[:int(t()-s)]+''.join(chr(random.randint(32,126))for _ in range(len(p)-int(t()-s))))
print(p)

Reads input from stdin. A 171-byte version runs under Python 2 (replaced input with raw_input):

import time,random
t=time.time
p,s=raw_input(),t()
while t()-s<len(p):print(p[:int(t()-s)]+''.join(chr(random.randint(32,126))for _ in range(len(p)-int(t()-s))))
print(p)

Ungolfed:

import random
import time

p = input()
start = time.time()
while time.time() - start < len(p): 
    print(
        p[:int(time.time() - start)] + 
        ''.join(chr(random.randint(32, 126)) for _ in range(len(p) - int(time.time()-start)))
    )
print(p)
Source Link

Python 3, 167 bytes

import time,random
t=time.time
p,s=input(),t()
while t()-s<len(p):print(p[:int(t()-s)]+''.join(chr(random.randint(32,126)) for _ in range(len(p)-int(t()-s))))
print(p)

Reads input from stdin. A 171-byte version runs under Python 2 (replaced input with raw_input):

import time,random
t=time.time
p,s=raw_input(),t()
while t()-s<len(p):print(p[:int(t()-s)]+''.join(chr(random.randint(32,126)) for _ in range(len(p)-int(t()-s))))
print(p)

Ungolfed:

import random
import time

p = input()
start = time.time()
while time.time() - start < len(p): 
    print(
        p[:int(time.time() - start)] + 
        ''.join(chr(random.randint(32, 126)) for _ in range(len(p) - int(time.time()-start)))
    )
print(p)