Question

A cyclist doubles his speed. How will his kinetic energy change: increase, decrease or remain same?

Answer 1

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`