A particle of mass 0.5 kg travels in a straight line with velocity v=ax^3 / 2, Where a=5 m^[(-

step 1 Here we have given a particle of mass 0 .5 kd travels in straight line with velocity function a

A particle of mass 0.5 kg travels in a straight line with...

A particle of mass $0.5 \mathrm{~kg}$ travels in a straight line with velocity $\mathrm{v}=\mathrm{ax}^{3 / 2}$, Where $\mathrm{a}=5 \mathrm{~m}^{[(-1) / 2]} \mathrm{s}^{-1}$. The work done by the net force during its displacement from $\mathrm{x}=0$ to $\mathrm{x}=2 \mathrm{~m}$ is (A) $50 \mathrm{~J}$ (B) $45 \mathrm{~J}$ (C) $25 \mathrm{~J}$ (D) None of these

A particle of mass $0.5 \mathrm{~kg}$ travels in a straight line with velocity $\mathrm{v}=\mathrm{ax}^{3 / 2}$, Where $\mathrm{a}=5 \mathrm{~m}^{[(-1) / 2]} \mathrm{s}^{-1}$. The work done by the net
force during its displacement from $\mathrm{x}=0$ to $\mathrm{x}=2 \mathrm{~m}$ is
(A) $50 \mathrm{~J}$
(B) $45 \mathrm{~J}$
(C) $25 \mathrm{~J}$
(D) None of these

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Key Concepts

Velocity as a Function of Position

When velocity is provided as a function of position instead of time, it allows for a direct computation of kinetic energy at different positions. This approach is useful because it enables one to find the change in kinetic energy over a displacement interval without needing to find the intermediate forces or accelerations explicitly.

Work-Energy Theorem

This principle states that the net work done on an object is equal to its change in kinetic energy. It provides a fundamental link between the forces acting on an object and its motion, allowing problems concerning work to be tackled by evaluating the initial and final kinetic energies rather than directly integrating force over displacement.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, given by the expression (1/2)mv², where m is the mass and v is the velocity. In problems involving variable velocity, determining the kinetic energy at different positions is essential for applying the work-energy theorem.

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