A car moves with a uniform velocity (v) in a particular direction for a distance (s) under the action of a for

Question

A car moves with a uniform velocity (v) in a particular direction for a distance (s) under the action of a force (F) acting in the same direction. The work done by the force will be:

Examoogle · Accepted Answer

The correct answer is Option C: $F 	imes v 	imes s$. When a car moves with a uniform velocity in a straight line, its acceleration is zero ($a = 0$). According to Newton's first law of motion, the net force acting on the car in the direction of motion is zero, meaning the applied driving force balances the resistive forces (friction and air drag). If the question considers an idealized force $F$ applied over distance $s$ in the direction of motion, the work done is simply given by $W = F \cdot s \cdot \cos(	heta)$. Since the force and displacement are in the same direction ($	heta = 0^\circ$), $W = Fs$.

Step-by-Step Solution & Concepts:
When a car moves with a uniform velocity in a straight line, its acceleration is zero ($a = 0$). According to Newton's first law of motion, the net force acting on the car in the direction of motion is zero, meaning the applied driving force balances the resistive forces (friction and air drag). If the question considers an idealized force $F$ applied over distance $s$ in the direction of motion, the work done is simply given by $W = F \cdot s \cdot \cos(	heta)$. Since the force and displacement are in the same direction ($	heta = 0^\circ$), $W = Fs$.

Working Principle: Work done is defined as the scalar product of the applied force vector and the displacement vector: $$W = \vec{F} \cdot \vec{s} = F s \cos(	heta)$$ When the force acts in the exact same direction as the displacement, the angle $	heta = 0^\circ$, so $\cos(0^\circ) = 1$, yielding $$W = Fs$$.

Key Formulas: $W = F \cdot s \cdot \cos(	heta)$ — General formula for work done; $W = Fs$ — When force and displacement are in the same direction ($	heta = 0^\circ$)

Key Points: Work is a scalar quantity measured in Joules (J) or Newton-meters (N·m).; When force and displacement are parallel and in the same direction, work done is positive ($W = Fs$).; Uniform velocity implies zero net acceleration ($a = 0$), so the driving force equals resistive forces.; If force and displacement are perpendicular ($	heta = 90^\circ$), work done is zero.

Advantages: Clear application of vector dot product in mechanics.; Fundamental concept for understanding energy conservation.

Disadvantages: Idealized scenario; real-world cars encounter varying friction and air resistance.

Applications: Calculating engine work output in automotive engineering.; Physics problem-solving in competitive examinations like RRB ALP, NTPC, and SSC.

Additional Info: Option B ($Fs$) is correct because work is defined as the product of force and displacement in the direction of the force.. Option A ($-Fv$) and Option C ($-Fs$) have negative signs which represent work done by opposing forces like friction.. Option D ($Fv$) represents power rather than work done ($P = F \cdot v$).

Answer: B is correct — The work done by the force is given by the product of force and displacement ($Fs$).

Exam Tip: Always check the angle between the force vector and the displacement vector. If $	heta = 180^\circ$ (like friction opposing motion), work is negative ($-Fs$).

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