Sense of zeropadding in a time domain
Shifting the data points (fftshift) and zero-padding the exact center of the FFT aperture has the property that all the even (symmetric) components with reference to the center of the original data set end up in the real part of the complex FFT result, and all the odd components end up in the imaginary part. e.g. the evenness to oddness ratio is preserved, which allows phase (with reference to the center of the window) to be easily interpolated. 

Being able to interpolate phase is important in the case of a zero-padded FFT because the zero-padding interpolates the spectral magnitude as well.  Since zero-padding results in an interpolated FFT result, that means that any original non-interpolated FFT result points will need to be interpolated from the zero-padded result.  Without an FFT shift of both the non-padded and zero-padded data, these interpolated results will be different from the non-interpolated FFT results (in phase).

This technique is a simple (homework or quiz level) result of the FT property that a shift in one domain is a complex frequency modulation in the other domain.