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Question
A cyclist doubles his speed. How will his kinetic energy change: increase, decrease or remain same?
Solution
As Kinetic energy K.E. = 1/2 Mv2
Since speed is doubled, its square will become 4 times
∴ K.E. increases i.e. become 4 times.
Or
K.E j = Mv2
When speed is doubled New speed v1 = (2 v)
New K.`E_2`= `1/2`M`V_1^2`
∴ New K.`E_2`= `1/2` M (2v`)^2`
K.`E_2`=`1/2` M 4`V^2`=4`[ 1/2M V^2]`
(¡¡) ÷ (¡)
=`(KE_2)/(KE_1)` =`(4[1/2MV^2])/([1/2 M V^2])`=`4/1`
=`(KE_2)/(KE_1)`
New K.`E._2`=4 Times K.`E_1`
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