  We calculate the survival probability P_S(t) up to time t of a tracer
particle moving along a deterministic trajectory in a continuous d-dimensional
space in the presence of diffusing but mutually noninteracting traps. In
particular, for a tracer particle moving ballistically with a constant velocity
c, we obtain an exact expression for P_S(t), valid for all t, for d<2. For d
\geq 2, we obtain the leading asymptotic behavior of P_S(t) for large t. In all
cases, P_S(t) decays exponentially for large t, P_S(t) \sim \exp(-\theta t). We
provide an explicit exact expression for the exponent \theta in dimensions d
\leq 2, and for the physically relevant case, d=3, as a function of the system
parameters.
