When a crack propagates with acceleration, deceleration and time rates of change of stress intensity factors, it is very important for us to understand the effects of acceleration, deceleration and time rates of change of stress intensity factors on the individual stresses and displacements at the crack tip. Therefore, the crack tip stress and displacement fields for a transiently propagating crack along gradient in functionally graded materials (FGMs) with an exponential variation of shear modulus and density are developed and the characteristics of a transiently propagating crack from the fields are analyzed. The effects of the rate of change of the stress intensity factor and the crack tip acceleration on the individual stresses at the crack tip are opposite each other. Specially, the isochromatics (constant maximum shear stress) of Mode I tilt backward around the crack tip with an increase of crack tip acceleration, and tilt forward around the crack tip with an increase of the rate of change of the dynamic mode I stress intensity factor.