Sophia exerts a steady 40-N horizontal force on a 8-kg

box resting on a lab bench. The box slides against a horizontal
friction force of 24 N. Show that the box accelerates
at 2 m/s2.

a = (Fap-Ff)/M = (40-24)/8 = 2 m/s^2.

To determine the acceleration of the box, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. The formula for Newton's second law is:

F = ma

Where:
- F is the net force acting on the object,
- m is the mass of the object, and
- a is the acceleration of the object.

In this case, the net force acting on the box is the difference between the force applied by Sophia and the frictional force. So we have:

F_net = F_applied - F_friction

Given:
- F_applied = 40 N (force applied by Sophia)
- F_friction = 24 N (frictional force)
- m = 8 kg (mass of the box)

Substituting these values into the equation, we get:

F_net = 40 N - 24 N
F_net = 16 N

Now, rearranging the formula to solve for acceleration (a), we have:

a = F_net / m

Substituting the values, we get:

a = 16 N / 8 kg
a = 2 m/s^2

Therefore, the box will accelerate at 2 m/s^2.