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It sounds like that the lecturer is saying

for the example we're discussing here, it would represent the distance of the car from its starting position. this should make more sense when you consider the change in the distance with respect at time, ie the slope of the distance time graph, ie how much distance you are covering per unit time, is just the speed.

Wiki gives this definition of derivative.

The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

Where "with respect to" is being used.

Is the lecturer saying "with respect at" or "with respect to"?

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    The speaker does not say "with respect at time", but "with respect to time". It sounds a little bit like at because the vowel in the speaker's "to" is a bit like a schwa, and he does not separate the t at the end of "respect" much from the next t at the start of "to". So there is no question to answer. – Weather Vane Aug 14 at 9:51
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    I'm voting to close this question as off-topic because its writer mis-heard the speaker. – Weather Vane Aug 14 at 9:56
  • One may look with respect at somebody, but one contemplates something with respect to something else. – Michael Login Aug 14 at 10:19
  • @WeatherVane I've updated the post, please mv your comments to answer, I'll accept it. Thanks you so much! – fu DL Aug 14 at 10:32
  • You've changed it to a different question, which is a matter of opinion. – Weather Vane Aug 14 at 10:36
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The lecturer said “with respect to time”, he didn't separate the "t" at the end of "respect" from the next "t" at the start of "to".

If you play the video at 0.25 speed, you'll get this clearly, and there's nothing like "at". Don't be mislead by the auto-generated transcript.

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