A toy car of mass 4 kg moves up a ramp under the influence of force F plotted against displacem

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A toy car of mass 4 kg moves up a ramp under the influence...

A toy car of mass $4 \mathrm{~kg}$ moves up a ramp under the influence of force $\mathrm{F}$ plotted against displacement $\mathrm{x}$. The maximum height attained is given by (Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ ) (A) $\operatorname{ymax}=5 \mathrm{~m}$ (B) $\operatorname{ymax}=8 \mathrm{~m}$ (C) $\operatorname{ymax}=15 \mathrm{~m}$ (D) ymax $=20 \mathrm{~m}$

A toy car of mass $4 \mathrm{~kg}$ moves up a ramp under the influence of force $\mathrm{F}$ plotted against displacement $\mathrm{x}$. The maximum height attained is given by (Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ )
(A) $\operatorname{ymax}=5 \mathrm{~m}$
(B) $\operatorname{ymax}=8 \mathrm{~m}$
(C) $\operatorname{ymax}=15 \mathrm{~m}$
(D) ymax $=20 \mathrm{~m}$

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Key Concepts

Work-Energy Theorem

The work-energy theorem states that the total work done on an object is equal to its change in kinetic energy. When applied to situations where the kinetic energy is converted into gravitational potential energy, this theorem helps relate the work done by forces (obtained from the area under a force-displacement graph) to the maximum height an object can reach.

Work Done by a Force

Work done by a force is the energy transferred when a force acts on an object over a displacement. When force varies with displacement, the work is found by calculating the area under the force versus displacement graph, which represents the integral of force with respect to distance.

Gravitational Potential Energy

Gravitational potential energy is the energy stored in an object due to its position in a gravitational field. It is calculated using the formula U = mgy, where m is the mass, g is the gravitational acceleration, and y is the height. This energy represents the work required to raise the object to a certain height against gravity.

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