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practiceM1b

practiceM1b - ≤ t< ∞ 3 Find the curvature of r t = t...

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Math 265 (Butler) Practice Midterm I – B Try to answer the following questions without the use of book, notes or calculator. Time yourself and try to finish the test in less than 50 minutes. 1. Find the projection of h 2 s, 1 , s - 1 i onto the vector h- 2 t, 5 - t 2 , 4 t i . 2. A particle travels along the parametric curve h e - t cos t, e - t sin t i starts at (1 , 0) at time t = 0 and then spirals into the origin (0 , 0) as t → ∞ . How far will the particle have traveled when it reaches the origin? (In other words, what is the arc length of the parametric curve for 0
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Unformatted text preview: ≤ t < ∞ .) 3. Find the curvature of r ( t ) = t i + 1 2 t 2 j + 2 √ 2 3 t 3 / 2 k at time t = 2. 4. A particle moving in three space as acceleration a ( t ) = h 2 , sin( πt ) , 6 t i . At time t = 0 the particle is at h 3 , , 1 i while at time t = 2 the particle is at h 1 ,-2 , 5 i . What is the velocity of the particle at time t = 1? 5. Find the the line in parametric form which is tangent to the curve x = 2 t 2 + t , y = 2 t 2 , z = t 3-t at time t = 2....
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