Survival probability of a ballistic tracer particle in the presence of diffusing traps

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> or =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) approximately exp(-theta t). We provide an explicit exact expression for the exponent theta in dimensions d< or =2 and for the physically relevant case, d=3, as a function of the system parameters.