Define the formula for work done by a constant force.

The work done ($W$) by a constant force ($F$) acting over a distance ($d$) in the direction of the force is given by:

$$W = Fd$$

For cart A:

• Applied force $F_A = F$
• Distance traveled $d_A = d$ So, the work done on cart A is:

$$W_A = F_A d_A = Fd$$

For cart B:

• Applied force $F_B = 2F$
• Distance traveled $d_B = d$ So, the work done on cart B is:

$$W_B = F_B d_B = (2F)d = 2Fd$$

We have $W_A = Fd$ and $W_B = 2Fd$.
Substitute $W_A$ into the expression for $W_B$:

$$W_B = 2(Fd)$$ $$W_B = 2W_A$$

This relationship matches option e.

The final answer is $\text{e. } W_B = 2W_A$.