Also Check - Tangential Velocity Formula
Understanding the Formula
The formula demonstrates that as the relative velocity (v) between two observers increases, the time experienced by the moving observer (Δt) expands or dilates. This formula underscores the crucial role of the speed of light (c) in these computations.Also Check - Horsepower Formula
Question 2: A particle is accelerated to 99.5% of the speed of light in a particle accelerator. If observed from a stationary laboratory, how much time will elapse on the particle's clock for every 1 minute on the lab's clock? Step 1: Determine the relative velocity v = 0.995c Step 2: Apply the Time Dilation formula Δt = Δt₀ / √(1 - (v² / c²)) Step 3: Substitute the values Δt = 1 minute / √(1 - (0.995)²) Step 4: Calculate Δt ≈ 22.37 minutesAlso Check - Shear Modulus Formula
Question 3: A spaceship is moving at 90% of the speed of light. How much time passes on the spaceship for every 8 years that pass on Earth? Step 1: Determine the relative velocity v = 0.90c Step 2: Apply the Time Dilation formula Δt = Δt₀ / √(1 - (v² / c²)) Step 3: Substitute the values Δt = 8 years / √(1 - (0.90)²) Step 4: Calculate Δt ≈ 24.99 years For every 8 years on Earth, approximately 24.99 years pass on the spaceship. Question 4: A particle is accelerated to 99.9% of the speed of light in a particle accelerator. How much time elapses on the particle's clock for every 2 minutes on the lab's clock? Step 1: Determine the relative velocity v = 0.999c Step 2: Apply the Time Dilation formula Δt = Δt₀ / √(1 - (v² / c²)) Step 3: Substitute the values Δt = 2 minutes / √(1 - (0.999)²) Step 4: Calculate Δt ≈ 44.72 minutes For every 2 minutes on the laboratory clock, approximately 44.72 minutes pass on the particle's clock. Question 5: A rocket is moving at 80% of the speed of light. How much time passes on the rocket for every 5 years that pass on Earth? Step 1: Determine the relative velocity v = 0.80c Step 2: Apply the Time Dilation formula Δt = Δt₀ / √(1 - (v² / c²)) Step 3: Substitute the values Δt = 5 years / √(1 - (0.80)²) Step 4: Calculate Δt ≈ 8.75 years For every 5 years on Earth, approximately 8.75 years pass on the rocket. Question 6: A spaceship is moving at 99.5% of the speed of light. How much time passes on the spaceship for every 2 years that pass on Earth? Step 1: Determine the relative velocity v = 0.995c Step 2: Apply the Time Dilation formula Δt = Δt₀ / √(1 - (v² / c²)) Step 3: Substitute the values Δt = 2 years / √(1 - (0.995)²) Step 4: Calculate Δt ≈ 10.10 years For every 2 years on Earth, approximately 10.10 years pass on the spaceship. Question 7: A high-speed train is traveling at 90% of the speed of light. How much time will elapse on the train for every 15 minutes that pass on a station's clock? Step 1: Determine the relative velocity v = 0.90c Step 2: Apply the Time Dilation formula Δt = Δt₀ / √(1 - (v² / c²)) Step 3: Substitute the values Δt = 15 minutes / √(1 - (0.90)²) Step 4: Calculate Δt ≈ 43.30 minutes For every 15 minutes on the station's clock, approximately 43.30 minutes elapse on the train. Question 8: A spaceship is moving at 99% of the speed of light. How much time passes on the spaceship for every 3 years that pass on Earth? Step 1: Determine the relative velocity v = 0.99c Step 2: Apply the Time Dilation formula Δt = Δt₀ / √(1 - (v² / c²)) Step 3: Substitute the values Δt = 3 years / √(1 - (0.99)²) Step 4: Calculate Δt ≈ 14.14 years For every 3 years on Earth, approximately 14.14 years pass on the spaceship. Question 9: A particle is accelerated to 99.99% of the speed of light in a particle accelerator. How much time elapses on the particle's clock for every 1 hour on the laboratory clock? Step 1: Determine the relative velocity v = 0.9999c Step 2: Apply the Time Dilation formula Δt = Δt₀ / √(1 - (v² / c²)) Step 3: Substitute the values Δt = 1 hour / √(1 - (0.9999)²) Step 4: Calculate Δt ≈ 141.43 hours For every 1 hour on the laboratory clock, approximately 141.43 hours elapse on the particle's clock. Question 10: A spaceship is moving at 75% of the speed of light. How much time passes on the spaceship for every 4 years that pass on Earth? Step 1: Determine the relative velocity v = 0.75c Step 2: Apply the Time Dilation formula Δt = Δt₀ / √(1 - (v² / c²)) Step 3: Substitute the values Δt = 4 years / √(1 - (0.75)²) Step 4: Calculate Δt ≈ 6.93 years For every 4 years on Earth, approximately 6.93 years pass on the spaceship. Time Dilation serves as a captivating testament to the relativity of time, underpinning its relevance and application in modern physics. Understanding the formula and its real-world implications is pivotal for comprehending the intricacies of Einstein's theory. Time Dilation demonstrates the extraordinary and often counterintuitive nature of our universe.