P2F10-Tut4-soln

# P2F10-Tut4-soln - Tutorial#3 1 You challenge your friend to...

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Tutorial #3 October 18, 2010 1. You challenge your friend to a race. You are startled by a car backFring, and start 0.5s before your friend. Your acceleration is 2.00 m/s 2 . Your friend’s acceleration is 2.20 m/s 2 . a) How long does it take your friend to pass you? b) How far are you from the starting line when your friend passes you? c) What is your velocity, and your friend’s velocity, at the moment your friend passes you? 2. A watermelon is dropped (initial velocity v 0 =0 ) from the top of a 20m cli±. At the same time the watermelon is dropped, a person at the bottom of the cli± shoots an arrow up towards the watermelon. The arow strikes the watermelon after 0.80s. a) At what distance from the base of the cli± does the arrow strike the watermelon? b) What was the arrow’s initial velocity? 3. This is just a quick review of basic calculus. a) ²ind the x -derivatives of the following functions (compute d dx f ( x ) for each function): f ( x )=5 x 5 - 3 x 3 + x f ( x )= e c cos( x ) , where c is independent of x f ( x, y ) = cos ( xy ) , where y is independent of x b) ²ind the anti-derivatives of the following functions: f ( y y 5 - 3 y 3 + y f ( x, y ) = cos ( xy ) , where x is independent of y c) Compute the deFnite integrals of the two functions from part (b) from y to y =1 . 4. Consider the function f ( x )=( x - 1) e - x 2 . a) ²ind the maximum and minimum values of the function. b) ²ind the equation of the tangent to the curve f ( x ) vs. x at the point x . 5. The position of a particle is given by the function x ( t t 3 - 3 t 2 +2 t . a) What is the intantaneous velocity and instantaneous acceleration of the particle as a function of time? b) The in³ection point of a graph is deFned as a point where the curvature (second derivative) changes sign. An in³ection point is either a maximum or a minimum of the derivative of the function. At what time does the position have an in³ection point? Is this point a maximum or minimum of the velocity?

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P2F10-Tut4-soln - Tutorial#3 1 You challenge your friend to...

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