A physics student measures the speed of a small car on a track. For the first 20 seconds, it travels at 5 m/s, and for the next 30 seconds, it accelerates to 8 m/s. How far does the car travel in total?

["Title: Physics in Action: Measuring Distance Traveled by a Small Car on a Track", "Meta Description:\nA physics student calculates the total distance traveled by a small car accelerating from 5 m/s to 8 m/s over two time intervals. Learn how to apply motion equations to real experiments.", "---", "### Tracking Motion: How a Physics Student Measures Distance", "In the world of physics experiments, understanding motion is fundamental. Recently, a dedicated student applied core kinematic principles to measure how far a small car travels on a track. This measurement involves analyzing constant and variable acceleration over two distinct time phases. Here’s a detailed breakdown of how the distance was calculated—and why this experiment matters for anyone studying mechanics.", "---", "### The Force of Motion: Two Phases of Movement", "The student observed the car traveling in two phases:", "- Phase 1: Constant speed of 5 m/s for 20 seconds\n- Phase 2: Accelerated uniformly from 5 m/s to 8 m/s over 30 seconds", "To find the total distance traveled, we calculate the distance covered in each phase using physics formulas.", "---", "### Phase 1: Constant Velocity", "When an object moves at a constant speed, the distance is simply:", "[\n\ ext{Distance}_1 = \ ext{Speed} \ imes \ ext{Time}\n]", "Plugging in the values:\n[\n\ ext{Distance}_1 = 5,\ ext{m/s} \ imes 20,\ ext{s} = 100,\ ext{meters}\n]", "---", "### Phase 2: Uniform Acceleration", "For the second phase, the car accelerates from 5 m/s to 8 m/s over 30 seconds. To find distance under uniform acceleration, we use:", "[\n\ ext{Distance}_2 = v_i \cdot t + \frac{1}{2} a \cdot t^2\n]", "where\n- ( v_i = 5,\ ext{m/s} ) (initial speed)\n- ( v_f = 8,\ ext{m/s} ) (final speed)\n- ( t = 30,\ ext{seconds} )\n- Acceleration ( a = \frac{v_f - v_i}{t} = \frac{8 - 5}{30} = \frac{3}{30} = 0.1,\ ext{m/s}^2 )", "Now apply the formula:\n[\n\ ext{Distance}_2 = (5 \ imes 30) + \frac{1}{2} \ imes 0.1 \ imes 30^2\n]\n[\n= 150 + 0.05 \ imes 900 = 150 + 45 = 195,\ ext{meters}\n]", "---", "### Total Distance Traveled", "Adding both phases:\n[\n\ ext{Total Distance} = \ ext{Distance}_1 + \ ext{Distance}_2 = 100,\ ext{m} + 195,\ ext{m} = 295,\ ext{meters}\n]", "---", "### Why This Experiment Matters", "This real-world example illustrates how motion analysis lays the foundation for advanced physics and engineering concepts. By breaking complex motion into measurable segments, students and researchers alike apply fundamental equations to predict and understand movement—key skills in automotive engineering, robotics, and sports dynamics.", "---", "Key Takeaways:\n- Constant speed motion uses simple multiplication.\n- Accelerated motion requires kinematic equations like ( \ ext{Distance}_2 = v_i t + \frac{1}{2} a t^2 ).\n- Segmenting motion into phases enables accurate distance calculations.", "For physics students and curious minds, every experiment is a step toward unlocking the secrets of motion.", "---", "Keywords:\nphysics student measures speed, small car motion experiment, distance traveled kinematics, uniform acceleration calculator, physics track experiment, constant velocity distance, kinematics problems, physics student project", "Updated: April 2025 —a practical reminder how physics turns movement into measurable science.", "---", "Try calculating similar problems yourself—physics becomes much clearer when you visualize motion in chunks!"]