1.which of newton's laws describe the mathematical relationship between force, mass, and acceleration
and
2.for an object to accelerate it must be acted on by what force

1. By Newton's second law, the mathematical relationship between force, mass and acceleration can be described.

2. An object will undergo acceleration only when an unbalanced force will be acting on any object.

Explanation:

1. The mathematical relationship between force, mass and acceleration is done in the Newton's second law of motion. In this law, it is stated that any external unbalanced force acting on any object will be equal to the rate of change of momentum. In other words, the external unbalanced force will be proportional to the acceleration exerted on the object and also to the mass of the object.

Since, momentum p = mass * velocity = mv

Since, the mass will be constant, dm/dt = 0, so F = ma

2. Also from this law, it can be understood that an object will undergo acceleration only when an unbalanced force will be acting on any object.