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Chapter 2: Problem 26

An airplane's takeoff speed is \(320 \mathrm{km} / \mathrm{h}\). If its average acceleration is \(2.9 \mathrm{m} / \mathrm{s}^{2},\) how much time is it accelerating down the runway before it lifts off?

Short Answer

Expert verified
The airplane takes approximately 30.7 seconds to accelerate down the runway before it lifts off.

Step by step solution

01

Convert the Speed Unit

The speed of the airplane is given in km/h that should be converted into m/s for uniformity of units because the acceleration is mentioned in m/s^2. The conversion factor is that 1 km/h = 0.278 m/s. Therefore, the takeoff speed in metres per second is \(320 \times 0.278 = 89.0 \mathrm{m} / \mathrm{s}\).
02

Use Definition of Acceleration

Acceleration is defined as the change in velocity per unit time i.e., acceleration \( = \frac{{final velocity - initial velocity}}{{time}}\). In our case, the airplane starts from rest, so the initial velocity is 0 m/s and the final velocity is 89.0 m/s.
03

Calculate Time

Rearrange the acceleration equation to solve for time. Time \(= \frac{{final velocity - initial velocity}}{{acceleration}}\). Plug in the given quantities for the final velocity(89.0 m/s), initial velocity(0 m/s) and acceleration(2.9 m/s^2) to find: time = \( \frac{{89.0 - 0}}{{2.9}} = 30.7\) seconds. So, the airplane takes approximately 30.7 seconds to accelerate down the runway before it lifts off.

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