If a man increase his speed by 2m/s, his K.E. is doubled, the original speed of the man is

Explanation

Man possesses kinetic energy, because of its velocity (v). If m is mass of man, then
`K=(1)/(2)mv^(2)`
Given, `" " v_(1)=v, m_(1)=m_(2)=m`,
When `" " v_(2)=(v+2)ms^(-1)`
Then `" " K_(2)=2K_(1)`
`:.(K_(1))/(K_(2))=(v_(1)^(2))/(v_(2)^(2))implies(K_(1))/(2K_(1))=(v^(2))/(v+2)^(2)impliesv^(2)-4v-4=0`
This gives, `v_(1)=(4+sqrt((16+16)))/(2)=(4+sqrt(32))/(2)`
`v_(1)=2(sqrt2+1)ms^(-1)`