There are (one can say) three coequal theories of motion for a single particle: Newton’s second law, stating that the total force on the particle causes its acceleration; the work-kinetic energy theorem, stating that the total work on the particle causes its change in kinetic energy; and the impulse-momentum theorem, stating that the total impulse on the particle causes its change in momentum. In this problem, you compare predictions of the three theories in one particular case. A $$3.00-kg$$ object has velocity $$7.00\hat{j}\ m/s$$. Then a constant net force $$12.0\hat{i}N$$ acts on the object for $$5.00\ s$$.
Calculate its acceleration from $$\vec{a}$$ = $$\frac{(\vec{v_f} - \vec{v_i})}{\Delta{t}}$$

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There are (one can say) three coequal theories of motion for a single particle: Newton’s second law, stating that the total force on the particle causes its acceleration; the work-kinetic energy theorem, stating that the total work on the particle causes its change in kinetic energy; and the impulse-momentum theorem, stating that the total impulse on the particle causes its change in momentum. In this problem, you compare predictions of the three theories in one particular case. A $$3.00-kg$$ object has velocity $$7.00\hat{j}\ m/s$$. Then a constant net force $$12.0\hat{i}N$$ acts on the object for $$5.00\ s$$.

Calculate its acceleration from $$\vec{a}$$ = $$\frac{(\vec{v_f} - \vec{v_i})}{\Delta{t}}$$

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There are (one can say) three coequal theories of motion for a single particle: Newtons second law, stating that the total force on the particle causes its acceleration; the work-kinetic energy theorem, stating that the total work on the particle causes its change in kinetic energy; and the impulse-momentum theorem, stating that the total impulse on the particle causes its change in momentum. In this problem, you compare predictions of the three theories in one particular case. A $$3.00-kg$$ object has velocity $$7.00\hat{j}\ m/s$$. Then a constant net force $$12.0\hat{i}N$$ acts on the object for $$5.00\ s$$.
Find the final kinetic energy from $$\dfrac{1}{2}mv_{f}^{2}=\dfrac{1}{2}m\vec{v}_{f}.\vec{v}_{f}$$.

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For a particle in rectilinear motion under constant acceleration the change in kinetic energy of a particle is equal to the work done on it by the net force.

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You can think of the work kinetic energy theorem as a second theory of motion, parallel to Newtons laws in describing how outside influences affect the motion of an object. In this problem, solve parts (a), (b), and (c) separately from parts (d) and (e) so you can compare the predictions of the two theories. A $$15.0g$$ bullet is accelerated from rest to a speed of $$780 m/s$$ in a rifle barrel of length $$72.0 cm$$. (a) Find the kinetic energy of the bullet as it leaves the barrel. (b) Use the workkinetic energy theorem to find the net work that is done on the bullet. (c) Use your result to part (b) to find the magnitude of the average net force that acted on the bullet while it was in the barrel. (d) Now model the bullet as a particle under constant acceleration. Find the constant acceleration of a bullet that starts from rest and gains a speed of $$780 m/s$$ over a distance of $$72.0 cm$$. (e) Modeling the bullet as a particle under a net force, find the net force that acted on it during its acceleration. (f) What conclusion can you draw from comparing your results of parts (c) and (e)?

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Assertion :The change in kinetic energy of a particle is equal to the work done on it by the net force. Reason: Change in kinetic energy of particle is equal to the work done only in case of a system of one particle.

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