. Show that in the frame of the
garage, the whole car can indeed enter the garage before its front
strikes the wall. Also calculate the length of the garage as seen by
the driver and prove that he expects to strike the wall 
seconds
before the back of the car gets in through the back of the garage.
Recalling that the maximum speed of propagation of information is
c, explain how the car fits into the garage before the news that
the front of the car has hit the garage wall reaches the back of the
car.
is given by
Show that for an observer at rest relative to 
[ i.e. with a
four- velocity 
], the particle's three- velocity 
can be written as
moving with velocity 
along the x- axis collides elastically with a stationary particle of
rest mass 
and as a result 
and 
are deflected through
angles 
and 
respectively. If E and 
are the
total energies of the particle 
before and after the collision
respectively, show that
and the four-
acceleration 
of a particle in Special Relativity and specify how
they relate to the Newtonian velocity 
and Newtonian acceleration
. If the rest mass of the particle is 
, what is its
four- momentum 
?
A particle moves with variable velocity 
relative to some inertial
frame, under the action of a force 
. Show that
where v is the magnitude of 
. Infer that
if the acceleration is parallel to 
, while
if the acceleration is perpendicular to 
.
Suppose the particle moves along the x- axis under a force of magnitude
being at rest at t=0. Show that the time taken to move to the point with
coordinate 
is
If you have any problems please come and see me or contact me by
email.
Peter Dunsby
