Work-energy principle: work equals force times parallel displacement

Steps:

• Recall the definition of work done by a force: integral of F dot ds, or F times displacement component parallel to F.
• For constant force, simplify to W = F * d * cosθ, where d is total displacement and θ is angle between F and displacement.
• When θ = 0 (force along displacement), cosθ = 1, so W = F * d, with d as distance in force's direction.
• Thus, q is the distance traveled in the direction of the force.

Why A is correct:

• Matches the physics definition: work W = F · s, where s is displacement vector; scalar product yields F times parallel component of distance.

Why the others are wrong:

• B: Perpendicular distance gives cos90° = 0, so no work done.
• C: Work formula uses displacement, not velocity; velocity relates to kinetic energy, not direct work calculation.
• D: Perpendicular velocity irrelevant; work depends on displacement direction, not speed components.

Final answer: A