Kinematics Equations Video Lessons

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Problem: 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 AA plane accelerates from rest at a constant rate of 5.00 m/s2 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 tTO 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 BWhat is the speed vTO 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 CWhat is the distance dfirst 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 DWhat is the distance dlast traveled by the plane in the last second before taking off? 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 EWhat 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.

FREE Expert Solution

The four UAM equations are:

 vf = v0 +atx= (vf+v02)tx= v0t+12at2 vf2= v02 +2ax

Part A

We have: 

  • tTO = ?
  • v0 = 0 m/s
  • a = 5.00 m/s
  • Δx = 1800 m
  • vf = ?
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Problem Details

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/s2 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 tTO 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 vTO 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 dfirst 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 dlast traveled by the plane in the last second before taking off? 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 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.

Frequently Asked Questions

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Our tutors have indicated that to solve this problem you will need to apply the Kinematics Equations concept. You can view video lessons to learn Kinematics Equations. Or if you need more Kinematics Equations practice, you can also practice Kinematics Equations practice problems.