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Question
Calculate the decrease in the kinetic energy of a moving body if its velocity reduces to half of the initial velocity.
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Solution
We know for kinetic energy, body must have velocity
Let initial velocity = v
Also, Kinetic energy is equal to
K.E. = `1/2"m""v"^2`
given velocity decreased to half, so new velocity v'
v' = `"v"/2`
= K.Enew = `1/2 "m" xx ("v"/2)2`
= K.Enew = `1/2 "m" "v"^2/4`
∴ K.Enew = `("m""v"^2)/8`
Now, as asked, we need to find the decrease
Δ K.E = `("m""v"^2)/2 - ("m""v"^2)/8`
Δ K.E = `3/4"m""v"^2`
Kinetic energy will decrease by `3/4`th of initial kinetic energy.
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