If two shopping carts of equal mass are pushed by two different people, one act accelerates three times as fast as the other cart. describe the forces acting on each cart?

The force on the faster cart is 3 times the force on the slower cart

Explanation:

The relationship between force exerted on each cart (F), mass of the cart (m) and acceleration (a) is given by Newton's second law:

For cart A, we have

(1)

For cart B, we have

(2)

the problem says that the acceleration of one cart is 3 times the acceleration of the other one, so

Substituting into eq.(2):

So, if we divide (2) by (1), we find the ratio between the two forces:

so, the force on cart B is 3 times larger the force on cart A.