
82 Classical Mechanics
© 2010 Taylor & Francis Group, LLC
where we have applied the initial condition v
0
= 0 at t
0
= 0. It is easy to notice that the
shorter the burn time, the greater the velocity. Thus, a rocket burns its fuel as quickly as
possible during its takeoff.
PROBLEMS
1. A particle of mass m, which at time t = 0 has position x
0
and velocity v
0
, is being acted upon
by a sinusoidal force
F = F
0
sin(ωt – ϕ)
where F
0
, ω, and ϕ are constants. Find the equations for position and velocity for all posi-
tive time t.
2. A particle of mass m is whirled on the end of a string of length R. The motion is in a verti-
cal plane in the Earth’s g ...