Question

By what factor does the kinetic energy of a particle increase if the speed is increased by a factor of 3?

Answer 1

KE = 1/2mv^2
Since v is 3 times
Therefore
1/2m(3v)^2
= 1/2m9v^2
Therefore the kinetic energy becomes 9 times

Answer 2

Kinetic energy of a particle increases to a factor of 9 when the speed is increased by a factor of 3

We know, Kinetic Energy (K.E.) of a body is given as:

K.E. = (1/2) m × v²                                       ...(1)

where 'm' is the mass of the body

and, 'v' is the velocity of the body.

Similarly, for a particle having mass as 'm' and velocity v' is given as :

K.E.₂ = (1/2) m × v'²

Given that v' = 3v        [As velocity is increased 3 times as before]

So, K.E.₂ becomes = (1/2) m × (3v)²

=  (1/2) m × 9v²

= 9 [(1/2) m × v²]

= 9 × K.E.                     [From (1)]

Thus, Kinetic energy increases 9 times.