He doesn't have a lead foot, it just looks that way

Classical Mechanics Level 5

Since the speed of light is finite (equal to \(c=3 \times 10^8 (m/s)\)), when we observe an object that is moving with constant speed, it can actually appear to have an acceleration. We'll call this an "apparent acceleration". As an example, consider a car moving on a straight road with a constant velocity \(v=50~m/s\). An observer stands a distance \(d=5~m\) from the side of the road and watches the car. Find the maximum "apparent acceleration" in \(\mu m/s^2\) the observer sees as she watches the car approach her and then move away.

Hint: Can you figure out the position the observer believes the car is at at each instant in time?

Details and assumptions

  • 1 \((\mu m)=10^{-6} (m)\)

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