Something about second law of motion

There are more mistakes in the second law of motion but here has been informed about a mistake; see below and comment on this post:

Suppose a body is moving towards a point (P) from a point (O). Suppose the body has been moved by a constant regular force of 1 unit. Let the time taken by the force (as in usual meaning) on the body be 5 seconds. Let the body is in resistance less space and its velocity is 1 m/s. Let, write down the sequence of velocity in each interval according to Newton after applying the regular force respectively, such as:
1 m/s, 2 m/s, 3 m/s, 4 m/s, 5 m/s, 6 m/s

Let find the common difference (v') of the sequence of velocity in each interval:
1 m/s - 2 m/s = 1 m/s
2 m/s - 3 m/s = 1 m/s
3 m/s - 4 m/s = 1 m/s
4 m/s - 5 m/s = 1 m/s
5 m/s - 6 m/s = 1 m/s

It would be better to express the Newton's formula of the form F = m×v' than F = m×a, but both would be wrong.

Because, F ≠ mv', F ≠ mv't ≠ mdt, F ≠ ma, F ≠ mat etc.
And F = St,
or F = mRt




PLEASE ANALYSE CAREFULLY AND COMMENT !!!
THIS SIMPLE EXAMPLE HAS ALSO BEEN ABLE TO REFUTE THE SECOND LAW OF MOTION...

Which option given below would be better? Chose independently a correct option from below based on the example given above

In the second law of motion (F=ma), mass (m) should be multiplied by:

a. addition in displacement with respect to time interval (added displacement/time, or d+/t, or say vd or v')

b. addintion in velocity with respect to time interval (added velocity/time, or v+/t, or say a)

c. change in displacement with respect to time interval (added displacement/time, or d+/t, say vd or v')

d. change in velocity with respect to time interval (added velocity/time, or v+/t, say a)

[Note: If we replace 'F=ma' by 'F=md+', the corrected formula will also not be correct again, because 'F=mRt'. Here has been given such options (a, b, c, d) only for information about some simple and easy basic mistakes of the second law of motion]

From the book: "REFUTATION AND SOLUTION OF SOME MISTAKES IN PHYSICAL SCIENCE": Copyright©: 2011, ISBN: 978-9937-2-3096-4 Gov. Regd. No. 598/067/68 (Nepal), pages: 718, Published by: Kathmandu Research and Publication Pvt. Ltd. Kathmandu, Nepal.