Trevor is pushing two boxes across a sidewalk. Box A has a mass of 4 kg. Box B has a mass of 8 kg. According to Newton's second law of motion, if Trevor applies the same amount of force to each box,

Question

A.
box B will move twice the distance of box A.
B.
box A will accelerate at twice the rate of box B.
C.
box B will accelerate at twice the rate of box A.
D.
box A and box B will accelerate at the same rate.

Answer 1

According to Newton's second law of motion, the acceleration (a) of an object is given by the equation:

\[ a = \frac{F}{m} \]

where \( F \) is the net force applied to the object, and \( m \) is the mass of the object.

In this case, if Trevor applies the same amount of force \( F \) to both boxes:

• For Box A (mass = 4 kg): \[ a_A = \frac{F}{4} \]

• For Box B (mass = 8 kg): \[ a_B = \frac{F}{8} \]

Now, comparing the accelerations:

• Box A's acceleration \( a_A = \frac{F}{4} \)
• Box B's acceleration \( a_B = \frac{F}{8} \)

Since \( \frac{F}{4} \) is twice \( \frac{F}{8} \), we can see that:

\[ a_A = 2 \cdot a_B \]

This means that box A will accelerate at twice the rate of box B.

Thus, the correct answer is:

B. box A will accelerate at twice the rate of box B.