To solve this problem, we will express the Force according to Newton's second Law, and acceleration, such as the change of velocity in the body by a certain distance, therefore,
The magnitude of the force is given as
F = ma
Where,
m = mass
a = Acceleration
That can be expressed as,

Replacing with our values we have
F = 0.140kg * (\frac{37+28.9}{1.85*10^{-3}})
F = 4987.03N
F= 4.9kN
Therefore the magnitude of the horizontal force is 4.9kN