A car accelerates uniformly from rest to 30 m/s in 10 seconds. Determine the distance traveled during this time.
["Title: How Uniform Acceleration Works: A Car Accelerating from Rest to 30 m/s in 10 Seconds", "---", "If a car starts from rest and accelerates uniformly to a speed of 30 meters per second in just 10 seconds, understanding how far it travels during this time involves fundamental physics principles. This scenario is a classic example of uniformly accelerated motion, widely studied in kinematics. In this article, we’ll break down the problem, calculate the acceleration, and determine the distance traveled — all key concepts for students and anyone interested in physics and automotive dynamics.", "---", "### Understanding Uniform Acceleration", "Uniform acceleration means the acceleration (rate of change of velocity) remains constant throughout the motion. In this case, a car begins with an initial velocity of 0 m/s (rest) and reaches 30 m/s in 10 seconds with no further changes in speed.", "---", "### Step 1: Calculate the Acceleration", "Use the basic kinematic equation for velocity under constant acceleration:", "[\nv = u + at\n]", "Where:\n- ( v ) = final velocity = 30 m/s\n- ( u ) = initial velocity = 0 m/s (starting from rest)\n- ( a ) = acceleration (unknown)\n- ( t ) = time = 10 seconds", "Substitute known values:", "[\n30 = 0 + a \ imes 10\n]", "[\na = \frac{30}{10} = 3 , \ ext{m/s}^2\n]", "The car accelerates at 3 m/s².", "---", "### Step 2: Calculate the Distance Traveled", "Use the equation for distance covered under constant acceleration starting from rest:", "[\ns = ut + \frac{1}{2} a t^2\n]", "Substitute values:\n- ( u = 0 , \ ext{m/s} )\n- ( a = 3 , \ ext{m/s}^2 )\n- ( t = 10 , \ ext{s} )", "[\ns = 0 \ imes 10 + \frac{1}{2} \ imes 3 \ imes (10)^2 = \frac{1}{2} \ imes 3 \ imes 100 = 150 , \ ext{meters}\n]", "---", "### Summary", "| Parameter | Value |\n|-----------------------|--------------------|\n| Initial velocity ((u)) | 0 m/s |\n| Final velocity ((v)) | 30 m/s |\n| Acceleration ((a)) | 3 m/s² |\n| Time ((t)) | 10 seconds |\n| Distance traveled ((s)) | 150 meters |", "---", "### Why This Matters", "Understanding how to compute distance under uniform acceleration is essential in physics, engineering, and vehicle dynamics. It helps in designing braking systems, estimating travel distances, analyzing performance, and teaching foundational mechanics.", "Next time you see a car smoothly speed up, remember: behind the numbers lies precise application of kinematic equations — turning motion into measurable science.", "---", "###キーワードまとめ\n- Uniform acceleration physics\n- Car acceleration from rest\n- Kinematic equations\n- Calculating distance in accelerated motion\n- Uniformly accelerated motion formula\n- Average velocity & distance under constant acceleration", "---", "If you found this explanation helpful, share it with fellow physics learners or engineers exploring classical mechanics. Understanding acceleration starts with a simple car ride — and leads to big insights!", "---", "Pointing toward real-world applications, mastering such calculations improves problem-solving skills beneficial in automotive technology, transportation planning, and academic physics studies."]
