Using \( s = ut + \frac{1}{2}at^2 \), with \( u = 0 \), \( v = at = 30 \), so \( a = 3 \, \text{m/s}^2 \), and \( t = 10 \):

["# Understanding Motion: How to Calculate Displacement Using ( s = ut + \frac{1}{2}at^2 )", "When analyzing motion under constant acceleration, one of the most powerful equations used is ( s = ut + \frac{1}{2}at^2 ). This formula helps determine the displacement ( s ) of an object moving with initial velocity ( u ), constant acceleration ( a ), and time ( t ). In this article, we’ll explore how to apply this equation using real values—specifically, when the initial velocity ( u = 0 ), the final velocity ( v = at = 30 , \ ext{m/s} ), acceleration ( a = 3 , \ ext{m/s}^2 ), and time ( t = 10 , \ ext{s} )—to calculate motion accurately.", "## Breaking Down the Variables", "### Given Quantities", "- Initial velocity, ( u = 0 , \ ext{m/s} )\n- Constant acceleration, ( a = 3 , \ ext{m/s}^2 )\n- Final velocity, ( v = at = 30 , \ ext{m/s} ) (note: ( v = 3 \ imes 10 = 30 , \ ext{m/s} ))\n- Time, ( t = 10 , \ ext{seconds} )", "### Understanding Why ( u = 0 ) and ( v = 30 , \ ext{m/s} )", "Since the object starts from rest (( u = 0 )), and accelerates uniformly at ( 3 , \ ext{m/s}^2 ), the standard kinematic relation ( v = u + at ) confirms:", "[\nv = 0 + (3 , \ ext{m/s}^2)(10 , \ ext{s}) = 30 , \ ext{m/s}\n]", "This consistent value validates our use of the displacement formula.", "## Applying the Displacement Formula: ( s = ut + \frac{1}{2}at^2 )", "Substitute ( u = 0 ), ( a = 3 , \ ext{m/s}^2 ), and ( t = 10 , \ ext{s} ):", "[\ns = (0)(10) + \frac{1}{2}(3)(10)^2\n]", "Calculate step by step:", "[\ns = 0 + \frac{1}{2}(3)(100) = \frac{1}{2}(300) = 150 , \ ext{meters}\n]", "So the object travels 150 meters in 10 seconds.", "## Physical Interpretation", "With constant acceleration starting from rest, the object speeds up uniformly. At 10 seconds, its velocity reaches 30 m/s, meaning it has significantly accelerated. Despite being under a moderate acceleration, full two-decade exposure leads to substantial displacement—highlighting how acceleration compounds over time.", "## Why This Equation Matters", "The equation ( s = ut + \frac{1}{2}at^2 ) is indispensable in physics for analyzing uniformly accelerated motion. With consistent initial velocity (often zero in introductory problems), it simplifies motion analysis and reveals the relationship between time, acceleration, and distance traveled.", "## Practical Example: Real-World Application", "Imagine a car accelerating from rest at a steady ( 3 , \ ext{m/s}^2 ). After 10 seconds, this model predicts it covers 150 meters—useful for understanding stopping distances, acceleration-based safety systems, or even sports motion tracking.", "## Summary", "- When ( u = 0 ) and ( v = at ), acceleration can be directly calculated from velocity and time.\n- Using ( s = ut + \frac{1}{2}at^2 ) with ( u = 0 ) simplifies to ( s = \frac{1}{2}at^2 ).\n- With ( a = 3 , \ ext{m/s}^2 ) and ( t = 10 , \ ext{s} ), the displacement is 150 meters.\n- This formula provides a clear, mathematically grounded method for analyzing constant acceleration scenarios.", "### Key Takeaway", "Mastering ( s = ut + \frac{1}{2}at^2 ) with simplified cases confirms the foundation of kinematics—enabling accurate predictions in physics and everyday motion analysis.", "---", "Key phrases for SEO:\n\( s = ut + \frac{1}{2}at^2 \), motion under constant acceleration, displacement calculation, factors of motion physics, acceleration formula example, physics formula explanation"]