x₁ = x₁ + v₁t + ² at ²₁ v₁ = v₁ + at, v² = v² + 2a4x, t Problem 1: Let's calculate some of the properties of the motion

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X X V T At V V At V V 2a4x T Problem 1 Let S Calculate Some Of The Properties Of The Motion 1 (57.76 KiB) Viewed 53 times

x₁ = x₁ + v₁t + ² at ²₁ v₁ = v₁ + at, v² = v² + 2a4x, t Problem 1: Let's calculate some of the properties of the motion for Elon Musk's Hyperloop idea. The Hyperloop is a high-speed underground train whose goal is to get from Los Angeles to San Francisco in 30 minutes. The distance from Los Angeles to San Francisco is 560 km. The motion consists of 3 parts: (0) start at rest and accelerate at a rate of g/2. travel at constant speed (iii) decelerate to rest at a rate of g/2. Here are some conversion factors:1 min = 60 sec, 1 km = 1000 m, 1 m/sec = 2.2 mi/hr. (a) Sketch a velocity vs. time graph of the motion. (b) For how long should the initial acceleration phase last? Answer: 65.9 sec (c) What is the largest speed the train will reach in miles/hour? Answer: 710/4 mi/hr Problem 2: A car starts from rest. A car reaches its maximum speed at t = 33.2 sec. The car has 3 different accelerations from t=0 sec to t = 33.2 sec. The acceleration is 9.7 m/sec² from t=0 sec to t = 5.1 sec. The acceleration is 3.9 m/sec² from t = 5.1 sec to t= 13.3 sec. The acceleration is 1.6 m/sec² from t = 13.3 sec to t = 33.2 sec. (a) What is the speed of the car at t = 33.2 sec? Answer: 113.3 m/sec (b) What is the total distance travelled by the car, after 33.2 sec? Answer: 2600.6 m Problem 3: A ball is dropped from rest from the top of a building. After the ball falls a distance h, it reaches the top of a window. The ball continues to fall, and it takes a time At = 0.4 sec to fall from the top of the window to the bottom of the window. The window has a vertical length L. = 2.0 m. What is the distance h from the top of the building to the top of the window? Answer: 0.47 m Vo = 0 m/sec (i) (ii) Window L = 2m At = 0.4 sec -b± √b²-4ac 2a h B