We'll consider the following kinematic equations:

$\overline{)\mathbf{}{{\mathit{v}}}_{{\mathit{f}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathbf{}}{\mathbf{+}}{\mathit{a}}{\mathit{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathit{x}}{\mathbf{=}}{\mathbf{}}\mathbf{\left(}\frac{{\mathit{v}}_{\mathit{f}}\mathbf{+}{\mathit{v}}_{\mathbf{0}}}{\mathbf{2}}\mathbf{\right)}{\mathit{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathit{x}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathit{t}}{\mathbf{+}}{\frac{1}{2}}{\mathit{a}}{{\mathit{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{\mathbf{}}{{{\mathit{v}}}_{{\mathit{f}}}}^{{\mathbf{2}}}{\mathbf{=}}{\mathbf{}}{{{\mathit{v}}}_{{\mathbf{0}}}}^{{\mathbf{2}}}{\mathbf{}}{\mathbf{+}}{\mathbf{2}}{\mathit{a}}{\mathbf{\u2206}}{\mathit{x}}}$

**Part A**

Applying the third kinematic equation from the set above, we have:

1800 = (0)(t) + (1/2)(5.00)(t^{2})

1800 = 2.5 t^{2}

To take off from the ground, an airplane must reach a sufficiently high speed. The velocity required for the takeoff, the takeoff velocity, depends on several factors, including the weight of the aircraft and the wind velocity.

**Part A.** A plane accelerates from rest at a constant rate of 5.00 m/s^{2} along a runway that is 1800 m long. Assume that the plane reaches the required takeoff velocity at the end of the runway. What is the time *t*_{TO} needed to take off? Express your answer numerically in seconds using three significant figures.

**Part B**. What is the speed *t*_{TO} of the plane as it takes off?

**Part C**. What is the distance d_{first} traveled by the plane in the first second of its run? Express your answer numerically in meters using three significant figures.

**Part D**. What is the distance d_{last} traveled by the plane in the last second before taking off? Express your answer numerically in meters using three significant figures.

**Part E**. What percentage of the takeoff velocity did the plane gain when it reached the midpoint of the runway? Express your answer numerically to the nearest percent.

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