13 v 135 s a 10 use the following the following

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Unformatted text preview: m , = 53.13° , v = 135◦ s a 10 ˙ Use the following the following parameters in your analysis:!R = 75 m, θ = 20 m ,/ v =nd m/s and v = -6 m/s . ! v = !2 m / s 2 . Chapter I: Particle Kinematics Homework I-5 Homework 1.B.1 Given: A particle P moves in three-dimensional space on a surface given by z = x2 y , where x = t2 /2 and y = 3 cos 2πt. Find: For time t = 1 s, determine the velocity and acceleration vectors of P in terms of their Cartesian coordinates. I-6 Chapter I: Particle Kinematics Homework Homework 1.B.2 Given: A particle P moves on a three-dimensional path given by R = θ2 , θ = t/2 and z = cos πt. Find: For time t = 1 s, determine the velocity and acceleration vectors of P in terms of their cylindrical coordinates. Chapter I: Particle Kinematics Homework I-7 Homework 1.C.1 Given: A particle P travels in the x-y plane with a path whose coordinates are given as a function of time t as: x (t) = 16 − 12t and y (t) = 2 + 15t − 3t2 . Find: For this problem: • Determine the velocity and acceleration of P in terms of their x-y components. • Make a sketch of the velocity and acceleration vectors for P. • Determine the rate of change of speed of P and the radius of curvature for the path of P. Use the following parameters in your analysis: t = 10 s. I-8 Chapter I: Particle Kinematics Homework Homework 1.C.2 Given: A particle P moves within a plane with a path given in terms of the polar coordinates of: R = 2θ2 , where R and θ are as defined below in the figure, and with R and θ given in meters and in radians, respectively. mework Problems ME 274 Find: For this problem: • Determine the velocity and acceleration vectors of P in terms of their polar coordinates. s within a plane with a path given in terms of the polar coordinates of: • Make a sketch of the velocity and acceleration vectors for P. • Determine the rate of change of speed of P. • Is speed of and with R nd ! given in meters and in e as defined below in the fig...
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