A car accelerates uniformly from rest to 60 m/s in 10 seconds, then maintains constant speed for 20 seconds, and finally decelerates uniformly to rest in 5 seconds. What is the total distance traveled?

["Title: Analyzing Total Distance Traveled in a Three-Stage Car Motion Scenario", "When a car accelerates uniformly from rest, maintains constant speed, then decelerates uniformly to stop, understanding the motion phases is essential for calculating total distance traveled. This article breaks down the motion into three distinct stages and computes the total distance covered, combining physics principles with practical SEo optimization.", "---", "### The Three-Phase Motion Overview", "1. Uniform Acceleration Phase\n The car starts from rest (initial velocity = 0 m/s) and accelerates uniformly over 10 seconds to reach a final velocity of 60 m/s.\n2. Constant Speed Phase\n After accelerating, the car travels at a steady speed of 60 m/s for 20 seconds without changing velocity.\n3. Uniform Deceleration Phase\n Finally, the car decelerates uniformly to rest (0 m/s) over 5 seconds.", "These phases allow us to calculate distance using basic kinematic equations, which is critical for intelligent traffic modeling, automotive engineering, and physics education.", "---", "### Phase 1: Uniform Acceleration (0 to 60 m/s in 10 s)", "Use the formula for distance under uniform acceleration:", "[\nd = \frac{v_0 + v}{2} \cdot t\n]", "Where:\n- ( v_0 = 0 , \ ext{m/s} ) (starting from rest)\n- ( v = 60 , \ ext{m/s} ) (final velocity)\n- ( t = 10 , \ ext{s} )", "[\nd_1 = \frac{0 + 60}{2} \cdot 10 = 30 \cdot 10 = 300 , \ ext{meters}\n]", "---", "### Phase 2: Constant Speed (60 m/s for 20 s)", "At constant velocity, distance is:", "[\nd = v \cdot t\n]", "[\nd_2 = 60 \cdot 20 = 1200 , \ ext{meters}\n]", "---", "### Phase 3: Uniform Deceleration (60 m/s to 0 m/s in 5 s)", "Again using the uniform acceleration formula (deceleration is negative acceleration):", "[\nd = \frac{v_0 + v}{2} \cdot t = \frac{60 + 0}{2} \cdot 5 = 30 \cdot 5 = 150 , \ ext{meters}\n]", "---", "### Total Distance Traveled", "Adding all three phases:", "[\n\ ext{Total Distance} = d_1 + d_2 + d_3 = 300 + 1200 + 150 = 1650 , \ ext{meters}\n]", "---", "### Why This Matters (SEo & Practical Relevance)", "Understanding motion profiles helps in autonomous vehicle path planning, traffic flow analysis, and efficiency modeling. Whether for educational content, automotive simulations, or physics-based problem solving, breaking down multi-stage motion enhances accuracy.", "Key keywords for SEO optimization:\n- uniform acceleration distance\n- constant speed motion distance\n- deceleration motion calculation\n- total distance traveled in physics problems\n- kinematic equations application", "---", "Final Answer: The car travels a total distance of 1650 meters.", "---", "Reduce guesswork in mechanical systems—mastering physics integrates smoothly with real-world applications and search intent."]