A particle moves in the xy− plane according to the law x=at, y=bt2, where a>0, b>0. Determine the particle’s trajectory y(x) and sketch its graph. Determine the speed of the particle as a function of time. Find the angle ϕ between the velocity vector and the x−axis.

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A: The path is given as,r(t)=<t2,t3> So, the velocity and acceleration will be, respectively,…

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Q: Find the derivative, r'(t), of the vector function. r(t) = ( tan(2t), sec(5t),

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Q: A point, p, is moving with acceleration 6t j - k at time t. If at t 1, the coordinates of P are (1,…

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A: We can answer first question as per the honor policy. Please resubmit other parts as well to know…

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Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: Topic :- Calculus