At the instant shown car A is traveling with a speed of 108 km/hr and is decreas
ID: 1842696 • Letter: A
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At the instant shown car A is traveling with a speed of 108 km/hr and is decreasing its speed at a rate of 1 m/s^2. At the same instant car B is traveling on the Car A interchange curve at a speed of 72 km/hr and increasing its speed at a rate of 2.0 m/s^2. For each vehicle at half second intervals: Calculate and plot the positions of each car until Car B merges onto the straightaway. Plot as s f(x) for 0 lessthanorequalto t lessthanorequalto 300 m. Calculate and plot the distance the two cars are apart. (As f(t) for 0 lessthanorequalto t lessthanorequalto 12 s Calculate and plot the relative velocity and 30.0 relative acceleration of Car B relative to Car A. v vector _B/A = V vector_B - v_vector _A, a vector _B/A = a vector _B - a vector _A (magnitudes only) Plot as f (theta) for 30 degree lessthanorequalto theta lessthanorequalto 90 degree. Write a short description of what is occurring in this situation. Which car reaches the merge point first, which is going faster, when does Car B catch up with Car A (or vice versa), how close do the two cars com to each other, etc. Calculate when and how fast for each at the merge point and when the cars meet. Calculate merge point data accurately to 0.1 s Present your solution in a one page memo and format as before with: To, From: Date:, Subject: a short description of the problem brief but complete description of the situation Following the memo: graphs of data data table with correct unit headings, significant digits, etc problem solution and equation development.Explanation / Answer
In this example, sA and sB can be defined from fixed datum lines extending from the center of the pulley along each incline to blocks A and B. If the cord has a fixed length `tot, the position coordinates are related mathematically by the equation sA(t) + `CD + sB(t) = `tot Here, `CD is the length of cord passing over the arc CD of the pulley. Here, we are allowing for the blocks to move by allowing sA and sB to depend on time. `tot and `CD do not depend on time. Physics 170 203 Week 8, Lecture 3 5 Dependent motion cont’d The velocities of the block can be related by differentiating the position equation, taking into account that d dt `tot = 0 and d dt `CD = 0. sA(t) + sB(t) = 0 which tells us that vA(t) = vB(t) . Acceleration can be found by differentiating the velocity equation,
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