Please help!! i’ll mark you the brainliest answer A box of mass 4kg is being pulled along a rough surface to the right, as shown below. When F=8N, the box accelerates to the right 1m/s^2. If F is doubled to 16N, the acceleration of the box across the same rough surface will be:

A) 1m/s^2
B) 2 m/s^2
C) 3 m/s^2
D) 4 m/s^2
E) 0.5 m/s^2

Hi there!

Recall that:

∑F = ma

In the given situation, there is acceleration occurring in the horizontal direction, so there is a net force.

∑F = Fa (Force applied) - Fκ (Force due to kinetic friction)

We can plug in given values to solve for the frictional force:

ma = Fa - Fκ

(4)(1) = 8 - Fκ

4 = 8 - Fk

Fκ= 4N (negative since working opposite to acceleration)

Now, solve given the new force:

4a = 16 - 4

4a = 12

a = 3 m/s², Answer C.

what was the acceleration of the 2 kg cart?

⇒ 16.0 cm/s2

what was the acceleration of the 4 kg cart?

⇒ 8.1 cm/s2

what was the acceleration of the 6 kg cart?

⇒ 5.3 cm/s2