SUMMARY
The radius of curvature of the track at 6 seconds into the curve can be calculated using the relationship between horizontal acceleration and velocity. Given that the train enters the curve at 100 km/hr and decelerates to 15 km/hr over 12 seconds, the horizontal acceleration measured is 2 m/s². The radius of curvature (R) can be determined using the formula R = v²/a, where v is the velocity in m/s and a is the horizontal acceleration. At 6 seconds, the velocity is approximately 66.67 km/hr (or 18.52 m/s), resulting in a radius of curvature of approximately 174.6 meters.
PREREQUISITES
- Understanding of kinematics and motion equations
- Familiarity with the concept of radius of curvature
- Knowledge of unit conversions (km/hr to m/s)
- Basic principles of acceleration and deceleration
NEXT STEPS
- Study the relationship between velocity and radius of curvature in circular motion
- Learn about the equations of motion under constant acceleration
- Explore the effects of deceleration on train dynamics
- Investigate the application of accelerometers in measuring motion
USEFUL FOR
Students in physics or engineering courses, train system designers, and anyone interested in understanding the dynamics of vehicles on curved tracks.