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**Problem**: 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).

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###### Problem Details

The velocity of an airplane as a function of time can be written as **v**(t) = b**i **− 3ct^{2}**j** 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).

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