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Solution: The velocity of an airplane as a function of time can be written as  v(t) = bi − 3ct2j where b and c are positive constants. Provide your answers in terms of b, c, and t when necessary. [a] What are the SI units of b and c? [b] Find an expression for the position r(t) of the airplane as a function of time assuming that the airplane is at the origin at t = 0. [c] Find an expression for the acceleration a(t) of the airplane as a function of time [d] Find the trajectory of the airplane (y vs. x).  

Problem

The velocity of an airplane as a function of time can be written as  v(t) = b− 3ct2j where b and c are positive constants. Provide your answers in terms of b, c, and t when necessary.

[a] What are the SI units of b and c?

[b] Find an expression for the position r(t) of the airplane as a function of time assuming that the airplane is at the origin at t = 0.

[c] Find an expression for the acceleration a(t) of the airplane as a function of time

[d] Find the trajectory of the airplane (y vs. x).