What is the acceleration of a cabinet of mass 45 kilograms if jake and ted push it by applying horizontal force of 25 newtons and 18 newtons respectively in the same direction? (assume a flat, frictionless surface.)

Forces in a single plane can simply be added together to find the resultant force. They are both in the same direction so the signs are the same. Hence resultant force = 25 + 18 = 43N.

By Newton's 2nd Law of Motion (which, for constant mass, produces the relation F = ma), a = F/m = 43/45 = 0.95ms^-2 (2sf)

Since both horizontal forces are applied in the same direction:

Total = 25 N + 18 N = 43 N.

Since we are assuming a flat friction less floor, so there is no opposition to the 43N.

The 43 N  acts in full effect, because there is no friction.

From:

Force, F = ma

Where m = mass, a = acceleration

43 N = 45 kg * a

45a = 43

a = 43/45

a = 0.9555...

a≈ 0.956 m/s²

Acceleration is ≈  0.956 m/s²