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# If the k.e of a particle is tripled,by what factor has its speed increased?

AND THIS 1: If the speed of a particle is halved,by what factor does its k.e change?

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- The WolfLv 69 years agoFavorite Answer
let k and v be the initial kinetic energy and velocity

k = ½mv²

let K & V represent the new kinetic energy and velocity

I'll do second part first

if velocity is halved then V = ½v

so

K = ½mV² = ½m(½v)² = ½m(¼v²) = ¼(½mv²) = ¼k

reduced to a quarter the initial kinetic energy

..........

first part

rearrange equation

v = √(2k/m)

if k is tripled then K=3k

so

V = √(2K/m) = √(2(3k)/m) = √3(√(2k/m)) = √3 v

so velocity increases by √3

,..,,

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- gooberLv 79 years ago
If the k.e of a particle is tripled,by what factor has its speed increased? sqrt(3)

AND THIS 1: If the speed of a particle is halved,by what factor does its k.e change? 1/4

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