The change in speed of a photon with respect to time is 0 as photons travel at $c$ forever. If no change in speed exists, how can photons have momentum and acceleration? I guess they don't work like classical mechanics particles.
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Everything has momentum, even when acceleration is zero. Photons do not accelerate, they pop in and out of existence instantaneously and immediately travel at the speed of light. Their momentum and energy are proportional to their frequency.
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