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Chapter 2: Problem 24

A space shuttle's main engines cut off 8.5 min after launch, at which time its speed is \(7.6 \mathrm{km} / \mathrm{s} .\) What's the shuttle's average acceleration during this interval?

Short Answer

Expert verified
The average acceleration of the space shuttle during this interval is \(0.0149 \mathrm{km/s^2}\).

Step by step solution

01

Convert the time from minutes to seconds

Since the given time is in minutes, and we usually express velocity in terms of seconds, we need to convert 8.5 minutes into seconds: \(8.5 \mathrm{min} \times 60 \mathrm{s/min} = 510 \mathrm{s}\)
02

Identify the final and initial velocities

The final velocity of the shuttle is given as \(7.6 \mathrm{km/s}\). Since it's reasonable to assume that the shuttle started from rest, the initial velocity is 0.
03

Compute the average acceleration

Acceleration is defined as the change in velocity divided by the change in time. So the average acceleration (a) during this interval is: \(a = \frac{v_f - v_i}{t}\) plugging in our values: \(a = \frac{7.6 \mathrm{km/s} - 0}{510 \mathrm{s}} = 0.0149 \mathrm{km/s^2}\).

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