/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 149 The train passes point \(B\) wit... [FREE SOLUTION] | 91影视

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Chapter 12: Problem 149

The train passes point \(B\) with a speed of \(20 \mathrm{~m} / \mathrm{s}\) which is decreasing at \(a_{t}=-0.5 \mathrm{~m} / \mathrm{s}^{2}\). Determine the magnitude of acceleration of the train at this point.

Short Answer

Expert verified
The magnitude of the acceleration of the train at the given point is \(0.5 \mathrm{~m} / \mathrm{s}^{2}\)

Step by step solution

01

Identify Given Details

Identify and list the given values. The speed, \(v\), of the train is \(20 \mathrm{~m} / \mathrm{s}\) and the tangential acceleration, \(a_{t}\), is \(-0.5 \mathrm{~m} / \mathrm{s}^{2}\).
02

Equation for Magnitude of Acceleration

Recall the formula for magnitude of acceleration, \(a = \sqrt{{a_{t}}^2 + {a_{c}}^2}\).
03

Substituting the Given Values

As we only have tangential acceleration and no mention of any radial or centripetal acceleration, we assume it to be 0. Thus, we can substitute \(a_{c} = 0\) and \(a_{t}=-0.5 \mathrm{~m} / \mathrm{s}^{2}\) into the formula.
04

Compute the Magnitude of Acceleration

Calculate the magnitude of acceleration by applying the square, sum, and square root operations. \(a = \sqrt{{(-0.5)}^2 + {0}^2} = 0.5 \mathrm{~m} / \mathrm{s}^{2}\)

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Most popular questions from this chapter

Cars \(A\) and \(B\) are traveling around the circular race track. At the instant shown, \(A\) has a speed of \(90 \mathrm{ft} / \mathrm{s}\) and is increasing its speed at the rate of \(15 \mathrm{ft} / \mathrm{s}^{2}\), whereas \(B\) has a speed of \(105 \mathrm{ft} / \mathrm{s}\) and is decreasing its speed at \(25 \mathrm{ft} / \mathrm{s}^{2}\). Determine the relative velocity and relative acceleration of car \(A\) with respect to car \(B\) at this instant.

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