A 30kg student pushes a 20kg box on a frictionless surface. If student accelerates at 0.80 m/s^2, what is acceleration of the box. My question is why does the box accelerate in opposite direction of the boy, and how does the frictionless surface affect this question?

The total momentum must be conserved. If the boy slides away to the left, the box must move to the right, since momentum is a vector quantity.

thanks, why does total momentum need to be conserved?

The question says (remember newton's third law), so how does that come in to play, if u push a box shouldnt it just move in the direction u push it in. why does it accelerate in opposite direction of student

Thanks!!! :D

In this scenario, the box accelerates in the opposite direction of the student due to Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. When the student pushes the box, they exert a force on it, and in response, the box exerts an equal and opposite force on the student.

Here's how you can analyze the problem step by step to determine the acceleration of the box:

Step 1: Determine the force applied by the student on the box.
The force applied by the student can be calculated using Newton's second law of motion, which states that force (F) is equal to the mass (m) multiplied by the acceleration (a). In this case, the mass of the student is 30 kg and the acceleration is 0.80 m/s^2. So, the force applied by the student is F = 30 kg * 0.80 m/s^2 = 24 N.

Step 2: Recognize that the force applied by the student on the box is the same as the force experienced by the box.
According to Newton's third law of motion, the force exerted by the student on the box is equal in magnitude and opposite in direction to the force exerted by the box on the student. Therefore, the force experienced by the box is also 24 N.

Step 3: Use the force experienced by the box to calculate its acceleration.
The acceleration of an object can be determined using the formula a = F/m, where a is the acceleration, F is the force, and m is the mass of the object. In this case, the mass of the box is 20 kg and the force on it is 24 N. So, the acceleration of the box is a = 24 N / 20 kg = 1.2 m/s^2.

Regarding the frictionless surface, it's mentioned in the question that the surface is frictionless. A frictionless surface means that there is no resistance to the box's motion due to friction. Therefore, there are no additional forces acting on the box apart from those described above, and the acceleration of the box is solely determined by the force applied by the student.