The four UAM equations are:

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

**Part A**

We have:

**t**_{TO}= ?**v**_{0}= 0 m/s**a = 5.00 m/s****Δx = 1800 m**- v
_{f}= ?

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 in seconds using three significant figures.

If you need to use the answer from this part in subsequent parts, use the unrounded value you calculated before you rounded the answer to three significant figures. Recall that you should only round as a final step before submitting your answer.

Part B

What is the speed *v*_{TO} of the plane as it takes off? Express your answer numerically in meters per second using three significant figures.

If you need to use the answer from this part in subsequent parts, use the unrounded value you calculated before you rounded the answer to three significant figures. Recall that you should only round as a final step before submitting your answer.

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.

If you need to use the answer from this part in subsequent parts, use the unrounded value you calculated before you rounded the answer to three significant figures. Recall that you should only round as a final step before submitting your answer.

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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Based on our data, we think this problem is relevant for Professor Montgomery's class at Texas A & M University - Commerce.