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A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation v=α√x, where α is a constant. The total work done by all the forces applied on the particle during its displacement from x=0 to x=d, will be

Asked in JEE Main 9th April 1st Shift 2024 · Integrating a position-dependent force

• (1) 2mα²d
• (2) (md)/(2α²)
• (3) m/(2α²d)
• (4) (mα²d)/2

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives 2mα²d; it is four times the change in kinetic energy 1/2m(α√d)².
• (2) Comes from inverting α²; the speed grows with α, so the work must too.
• (3) Comes from inverting both α² and d; the work must grow with the distance covered.

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