Question

the velocity of a body moving in straight line increased by applying a constant force F for some distance in the direction of the motion Prove that the increase in the kinetic energy of the body is equal to the work done by the
force on the body
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Answer 1

$\huge{\mathfrak{Question:-}}$

The velocity of a body moving in straight line increased by applying a constant force F for some distance in the direction of the motion Prove that the increase in the kinetic energy of the body is equal to the work done by the  force on the body.

$\huge{\mathfrak{Solution:-}}$

The work-energy theorem states that the work done on a body is equal to the change in kinetic energy of the body.

Suppose a body of mass 'm' is under an acceleration 'a' due to which its initial speed 'u' at time t = 0 becomes final velocity 'v' at time t = t.

The distance travelled by the body in this can be found out using,

$\sf{v^{2}=u^{2}+2as}$

$\sf{Multiply\;both\;side\;by\;1/2\;m\;we\;have,}$

$\sf{1/2mv^{2}=1/2mu^{2}+mas}$

$\sf{\implies (ma)s=1/2mv^{2}-1/2mu^{2}}$

$\sf{\implies Work\;done=change\;in\;kinetic\;energy\;of\;the\;body.}$