A particle accelerates from rest at 4 m/s². Using the formula *distance* = ½ × *acceleration* × *time²*, how far does the particle travel in 10 seconds?
["How Far Does a Particle Travel When Accelerating from Rest?", "Understanding the motion of a particle accelerating from rest is a fundamental concept in physics. When an object starts at zero velocity and accelerates uniformly, its distance traveled can be precisely calculated using a well-known kinematic equation. This guide explains the formula and shows how to solve for distance traveled over a specific time.", "### The Motion Formula", "The key formula for distance traveled by a particle starting from rest under constant acceleration is:", "[\n\ ext{distance} = \frac{1}{2} \ imes \ ext{acceleration} \ imes \ ext{time}^2\n]", "Where:", "- Distance (d) is measured in meters (m),\n- Acceleration (a) is in meters per second squared (m/s²),\n- Time (t) is in seconds (s).", "### Given Values", "- Acceleration ( a = 4 , \ ext{m/s}^2 )\n- Time ( t = 10 , \ ext{s} )\n- Initial velocity is zero (starts from rest).", "### Applying the Formula", "Plug the values into the equation:", "[\nd = \frac{1}{2} \ imes 4 , \ ext{m/s}^2 \ imes (10 , \ ext{s})^2\n]", "Calculate step-by-step:", "1. Square the time: ( 10^2 = 100 )\n2. Multiply by acceleration: ( 4 \ imes 100 = 400 )\n3. Multiply by ½: ( \frac{1}{2} \ imes 400 = 200 )", "Thus,", "[\n\ ext{distance} = 200 , \ ext{m}\n]", "### Conclusion", "In 10 seconds, a particle that accelerates from rest at 4 m/s² travels 200 meters. This formula—distance = ½ × acceleration × time²—is essential for analyzing uniformly accelerated motion and forms the foundation of classical mechanics. Whether you're studying physics or solving practical problems, mastering this calculation helps you predict motion accurately.", "If you're interested in kinematics, exploring how acceleration, time, and distance interconnect will deepen your understanding of physical systems—from vehicles to particle physics experiments."]
