How Does Time Dilation Influence Perceived Velocity?

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SUMMARY

The discussion centers on the influence of time dilation on perceived velocity, particularly in the context of a car traveling on Earth and an observer in a spacecraft moving at 0.5c. The initial calculation shows the car's speed as 144 km/h based on Earth measurements. However, due to time dilation, the observer in the spacecraft perceives the car's speed as 1440 km/h, illustrating how relativistic effects alter velocity perception. The conversation also highlights the necessity of correcting the time dilation formula to 1/√(1-(v/c)²) and emphasizes the importance of considering length contraction from the spacecraft's perspective.

PREREQUISITES
  • Understanding of special relativity concepts, including time dilation and length contraction.
  • Familiarity with the velocity addition formula in relativistic physics.
  • Basic knowledge of the speed of light (c) and its significance in relativity.
  • Mathematical skills to manipulate square roots and fractions in physics equations.
NEXT STEPS
  • Study the corrected time dilation formula: t=1/√(1-(v/c)²).
  • Explore the implications of length contraction in relativistic scenarios.
  • Learn about the velocity addition formula in special relativity.
  • Investigate real-world applications of time dilation, such as GPS satellite technology.
USEFUL FOR

Physics students, educators, and anyone interested in the effects of relativity on motion and velocity perception.

AleksanderPhy
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Hello I have a question about how time effects velocity:So we have a car on Earth traveling 200m with 5 seconds we get that car moves 40m/s and 40x3600=144000 and 144000:1000=144km/h so car on Earth travels 144km/h now let's consider a that there is observer on spacecraft traveling 0.5c through time dilation formula:t=1/√1-v/c we get that observer on spacecraft get's that car travels 200m with 0.5 seconds so observer thinks that car goes 1440 km/h. Does this mean that time effects velocity?
 
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There's a mistake in your formula, it should be 1/√(1-(v/c)2). You also need to include the effect of length contraction but from the point of view of the spacecraft , the car is traveling at roughly 0.5c (at little more or a little less depending on the directions).

Velocity Addition Formula
 

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