I don't understand this explanation. I don't get how the new acceleration is 8, if we didnt know what the mass or net force was. Where did the 2 for force and 1 for mass come from?

Question

A cart is rolling down a hill at the rate of 2 m/s2. If the mass of the cart is cut in half and the net force

is doubled, what is the new acceleration?

I cant attach an image but this is what the explanation I was given, looks like:

a=2ms^2 F=ma F=ma

new a=4x=8m/s^2 (2)=(1)(2) (4)=(1/2)(8)

Answer 1

F = ma therefore, dividing both sides by "m", a = F/m and since a = 2, then F/m = 2

Doubling the force and cutting the mass in half gives:

a_new = (2F)/(m/2) = 4F/m

But the original F/m (acceleration) was 2 so plugging in F/m = 2 we get:

a_new = 4F/m = 4(2) = 8