how is acceleration of the cart related to the amount of force acting on it? the strips of it?
We know that Newton's Second Law of Motion states that -
[latex]F = ma[/latex]
It is clear that acceleration is directly proportional to the Force acting on a body. So, the amount of Force acting on a body is directly proportional to the acceleration, when the mass is constant.
Force on the cart is directly proportional to the acceleration.
This relationship was given be Sir Isaac Newton.
F = ma
Where F is force, a is acceleration and m is constant of proportionality , also known as mass.