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Recent studies into Weyl semimetals with noncentrosymmetric crystal structures have revealed a wide range of second order nonlinear phenomena, including the polarization-selective photogalvanic effect and giant second harmonic generation. We here present a study of another second order nonlinear effect, impulsive stimulated Raman scattering, in the type II Weyl semimetal T_d-WTe₂. Using ultrafast time-resolved optical reflectivity measurements, we demonstrate a large number of coherent phonons excited through this impulsive stimulated Raman scattering process and identify polarization-dependent selection rules for these phonons based on a symmetry analysis of the crystal structure of the material. Further, we investigate the fluence dependence of the phonons and compare this dependence to fluence-dependent carrier dynamics.