SUMMARY
The total distance traveled by an object moving along the x-axis, described by the position function x(t) = 2 + (3/π) - (3/π)(cos(π/3)t), can be determined by first calculating the derivative to find the speed, v. The critical points where v = 0 indicate changes in direction. By evaluating the position function at these critical points and calculating the absolute differences between consecutive x values, one can sum these absolute values to find the total distance traveled over the interval 0 ≤ t ≤ 4.5.
PREREQUISITES
- Understanding of calculus, specifically differentiation
- Familiarity with trigonometric functions and their properties
- Knowledge of absolute value calculations
- Ability to analyze motion along a one-dimensional axis
NEXT STEPS
- Study the process of finding derivatives of trigonometric functions
- Learn about critical points and their significance in motion analysis
- Explore the concept of absolute distance in one-dimensional motion
- Review applications of calculus in physics, particularly in motion problems
USEFUL FOR
Students studying calculus, physics enthusiasts, and anyone interested in understanding motion along a one-dimensional axis.