Final answer:
The total force needed to accelerate a 2.0 kg block at 4.0 m/s² against a frictional force of 10.0 N is 18.0 N, calculated by adding the force required to overcome friction and the force required for acceleration.
Step-by-step explanation:
To calculate the total force needed to accelerate a 2.0 kg block of wood at 4.0 m/s² along a rough table, against a force of friction of 10.0 N, we use Newton's second law, which states that the force is the product of the mass and the acceleration (F = ma). Since there is a force of friction acting against the motion, we need to add this to the force required to achieve the acceleration. Therefore, the force needed to overcome friction is already 10.0 N, and the additional force to produce the acceleration is calculated by multiplying the mass (2.0 kg) by the acceleration (4.0 m/s²), which gives us 8.0 N. Adding the two forces together gives us a total force of 18.0 N (10.0 N for friction + 8.0 N to accelerate), which corresponds to answer choice a) 18.0 N.