Dear Student,
As the force acting on the body is constant, its acceleration will also be constant.
Let initial velocity='u'
Let acceleration='a'
The distance travelled by a body undergoing consant acceleration in the nth second is given by
Sn=u + (a/2)(2n-1)-----------(1)
Hence according to question, S1=5m and S3=2m
From (1),
S1=u + (a/2)[2(1)-1]
or 5=u + a/2----------(2)
Also, S3=u + (a/2)[2(3)-1]
or 2=u + (5/2)a-----------(3)
Solving (2) and (3) for 'u' and 'a' we get,
u=33/6 and a=(-3/2)
Hence acceleration=a=-3/2 ms-2.
Mass of body = m = 4kg
Let force=F
Hence by 2nd law of motion,
F = ma
or F = 4(-3/2)
or F = -6N
Hence the magnitude of force is 6N and is acting opposite to the direction of motion of the body.
Regards,