By what factor will the kinetic energy of a particle change if the speed is increased by a factor of 4? 32 16 8 4
Question
By what factor will the kinetic energy of a particle change if the speed is increased by a factor of 4?
- 32
- 16
- 8
- 4
Solution
The kinetic energy of a particle is given by the formula KE = 1/2 mv^2, where m is the mass of the particle and v is the speed of the particle.
If the speed is increased by a factor of 4, the new speed will be 4v.
Substituting this into the kinetic energy formula gives KE = 1/2 m (4v)^2 = 1/2 m (16v^2) = 16 * (1/2 mv^2).
So, the kinetic energy of the particle will increase by a factor of 16.
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