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The position of a particle in the xy-plane at time t is r(t) = (et ) i + 3 e 16 j- Find an equation in x and y whose graph is the path of the particle. Then find the particle's velocity and acceleration vectors at t = In 2.The path r(t) = (t) i+ (2t- +3) j describes motion on the parabola y= 2x- + 3. Find the particle's velocity and acceleration vectors at t =5, and sketch them as vectors on the curve.The equation r(t) =(6 cost) i + (3 sin t) j+ (6t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors. Then write the particle's velocity at t = as a product of its speed and direction