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Chapter 2: Problem 56

An airplane starts from rest and accelerates at \(12.1 \mathrm{~m} / \mathrm{s}^{2}\). What is its speed at the end of a \(500 .-\mathrm{m}\) runway?

Short Answer

Expert verified
Answer: The speed of the airplane at the end of the 500m runway is approximately 110 m/s.

Step by step solution

01

Write down the given values

We know the following values: - Initial velocity (u) = 0 m/s - Acceleration (a) = 12.1 m/s² - Distance (s) = 500 m
02

Use the equation of motion

Now, we will use the equation v² = u² + 2as to find the final velocity (v).
03

Substitute the values and solve for v

Substitute the given values into the equation: v² = (0)² + 2(12.1)(500) Calculating the result: v² = 0 + 2(12.1)(500) v² = 12100 Now, find the square root of 12100 to get the final velocity (v): v = √12100 v ≈ 110 m/s
04

State the final answer

The speed of the airplane at the end of the 500m runway is approximately 110 m/s.

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Most popular questions from this chapter

You are flying on a commercial airline on your way from Houston, Texas, to Oklahoma City, Oklahoma. Your pilot announces that the plane is directly over Austin, Texas, traveling at a constant speed of \(245 \mathrm{mph}\), and will be flying directly over Dallas, Texas, \(362 \mathrm{~km}\) away. How long will it be before you are directly over Dallas, Texas?

Two cars are traveling at the same speed, and the drivers hit the brakes at the same time. The deceleration of one car is double that of the other. By what factor does the time required for that car to come to a stop compare with that for the other car?

Which of these statement(s) is (are) true? 1\. An object can have zero acceleration and be at rest. 2\. An object can have nonzero acceleration and be at rest. 3\. An object can have zero acceleration and be in motion. a) 1 only b) 1 and 3 c) 1 and 2 d) \(1,2,\) and 3

A stone is thrown downward with an initial velocity of \(10.0 \mathrm{~m} / \mathrm{s}\). The acceleration of the stone is constant and has the value of the free-fall acceleration, \(9.81 \mathrm{~m} / \mathrm{s}^{2} .\) What is the velocity of the stone after \(0.500 \mathrm{~s} ?\)

The 2007 world record for the men's 100 -m dash was \(9.77 \mathrm{~s}\). The third-place runner crossed the finish line in \(10.07 \mathrm{~s}\). When the winner crossed the finish line, how far was the third-place runner behind him? a) Compute an answer that assumes that each runner ran at his average speed for the entire race. b) Compute another answer that uses the result of Example 2.3, that a world- class sprinter runs at a speed of \(12 \mathrm{~m} / \mathrm{s}\) after an initial acceleration phase. If both runners in this race reach this speed, how far behind is the third-place runner when the winner finishes?
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