physics
posted by martini .
A particle has a kinetic energy equal to its rest energy.
(a) What is the speed of this particle?
(b) If the kinetic energy of this particle is doubled, does its speed increase by more than, less than, or exactly a factor of 2?
(c) Explain
(d) Calculate the speed of a particle whose kinetic energy is twice its rest energy.
I got (a) and (d)
(a) .866c and (d) .943c
but I'm stuck on (b) and (c) I think it might be less than 2 but I have no idea why that would be the case, can someone please explain it to me!? Thank you!

physics 
Elena
(a)
KE = m(o) •c^2•[1/sqrt(1β^2) 1],
E(o) = m(o) •c^2,
KE = E(o),
m(o) •c^2•[1/sqrt(1β^2) 1] =
= m(o) •c^2,
1/sqrt(1β^2) =2,
β = v/c = 0.866.
v = 0.866•c =0.866•3•10^8 =2.6•10^8 m/s.
(b),(c),(d)
KE = 2 •E(o)
m(o) •c^2•[1/sqrt(1β^2) 1] =
=2•m(o) •c^2,
1/sqrt(1β^2) =3,
β = v/c = 0.94.
v =0.94•c =2.82•10^8 m/s.
Respond to this Question
Similar Questions

physics kinetic energy
a) if a particle's speed decreases by a factor of four, by what factor does its kinetic energy change? 
physics
(Requires calculus) Prove the relativistic workenergy theorem in one dimension. The force exerted on a particle is given not by F=ma, but F=dp/dt. Using the expression for the relativistic momentum of a particle p=γmv, integrate … 
Physics
A single conservative force acts on a 5.00 kg particle. The equation Fx = (2x + 4) N describes this force, where x is in meters. As the particle moves along the x axis from x = 1.40 m to x = 5.80 m, calculate the following. (a) the … 
Physics
A single conservative force F(x) acts on a 1.6 kg particle that moves along an x axis. The potential energy U(x) associated with F(x) is given by U(x) = 2.9xex/3 where x is in meters. At x = 3.4 m the particle has a kinetic energy … 
Physics
A 245 g particle is released from rest at point A inside a smooth hemispherical bowl of radius 35.0 cm, as shown in Figure 521. (a) Calculate the gravitational potential energy at A relative to B. 1 . (b) Calculate the particle's … 
Physics 2
A particle moves along a line where the potential energy of its system depends on its position r as graphed in Figure P8.46. In the limit as r increases without bound, U(r) approaches +1 J. (a) Identify each equilibrium position for … 
Physics
The kinetic energy of a massive particle is equal to the energy of a photon. The massive particle moves at 1.49 % the speed of light. What is the ratio of the photon wavelength to the de Broglie wavelength of the particle? 
physics
A 278 g particle is released from rest at point A inside an smooth hemispherical bowl of radius 36.5 cm, as shown below. (a) Calculate the gravitational potential energy at A relative to B. J (b) Calculate the particle's kinetic energy … 
Physics
The kinetic energy of a particle is equal to the energy of a photon. The particle moves at 6.9% of the speed of light. Find the ratio of the photon wavelength to the de Broglie wavelength of the particle. Take the speed to be nonrelativistic. 
Physics
A particle of mass m kinetic energy K momentum p collides head on elastically with another particle of mass 2m at rest A) Momentum of first particle ?