The instantaneous position of an object is specified by its position vector leading from a fixed origin to the location of the object modeled as a particle. Suppose for a certain object the position vector is a function of time, given by r= 4 i + 3 j - 1t k, where r is in meters and t is in seconds.(a) Evaluate df/dt.j+ O R) m/s(b) What physical quantity does dř/dt represent about the object?O the acceleration vectorO the displacement vectorO the velocity vector

Rate of change of position vector is "Velocity Vector". Velocity is obtained by differentiating…

Answered: e instantaneous position of an object…

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Q/ A particle moves in an xy plane according to x(1)= -20.00 + 20.00t - 4.00 and y(t) = 25.00 + 17.00t -19.00², with x and y in meters and t in seconds. At t= 10 s, a. What is the particle velocity vector vì nunit vector notation? b. What is the particle acceleration vector đìn unit vector notation?
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r The speed of a boat in still water is V. A river flows with a speed of v₁. The boat travels distance of 14 miles downstream in a river in 1 hour. However, the return journey takes 2 hours. Calculate the V and V₁. Hint: Velocity = displacement/time. Displacement can be positive of neagtive depending on the direction. You will first need to set up the equations by taking into account the resultant velocity of the boat in flowing water. Consider the direction the river is flowing to be positive. Set up two equations, one for the downstream journey and one for the upstream journey, in terms of "V" and "v": Do V" and "v, add or substract downstream to give the resultant downstream velocity? Do v" and "v, add or substract upstream togive the resultant upstream velocity? Use the upstream direction as negative. The resultant upstream velocity should be negative. Equation 1 (downstream): Equation 2 (upstream): Solve for: V₁² vb Write an algebraic expression; do not use numerical values except…
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