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<meta name="description" content="A small body moves along a circle of radius r at a speed that increases linearly in time according to the law v = kt. Find the dependence of the total acceleration of the body on time.">
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<title>A small body moves along a circle of radius r at a speed that increases linearly in time according to the law v = kt. Find the dependence of the total acceleration of the body on time.</title>
$1.3.25.$ A small body moves along a circle of radius $r$ at a speed that increases linearly in time according to the law $v = kt$. Find the dependence of the total acceleration of the body on time.
</p>
<h3>Solution</h3>
<p>
<p>We will decompose the acceleration into two components, tangential $a_\parallel$ and normal $a_\perp$</p>
<p>In the longitudinal direction, the acceleration $a_\parallel$ is associated with the change in speed </p>
<p class="exp">
$$a_\parallel = k$$
</p>
<p>In the transverse direction, the acceleration $a_\perp$ is a consequence of the centrifugal force</p>
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<meta name="description" content="A small body moves along a circle of radius r at a speed that increases linearly in time according to the law v = kt. Find the dependence of the total acceleration of the body on time.">
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<meta property="og:description" content="A small body moves along a circle of radius r at a speed that increases linearly in time according to the law v = kt. Find the dependence of the total acceleration of the body on time.">
<meta property="og:description" content="A small body moves along a circle of radius r at a speed that increases linearly in time according to the law v = kt. Find the dependence of the total acceleration of the body on time.">
<title>A small body moves along a circle of radius r at a speed that increases linearly in time according to the law v = kt. Find the dependence of the total acceleration of the body on time.</title>
<title>A small body moves along a circle of radius r at a speed that increases linearly in time according to the law v = kt. Find the dependence of the total acceleration of the body on time.</title>
$1.3.25.$ A small body moves along a circle of radius $r$ at a speed that increases linearly in time according to the law $v = kt$. Find the dependence of the total acceleration of the body on time.
$1.3.25.$ A small body moves along a circle of radius $r$ at a speed that increases linearly in time according to the law $v = kt$. Find the dependence of the total acceleration of the body on time.
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
<p>We will decompose the acceleration into two components, tangential $a_\parallel$ and normal $a_\perp$</p>
<p>We will decompose the acceleration into two components, tangential $a_\parallel$ and normal $a_\perp$</p>
<p>In the longitudinal direction, the acceleration $a_\parallel$ is associated with the change in speed </p>
<p>In the longitudinal direction, the acceleration $a_\parallel$ is associated with the change in speed </p>
<p class="exp">
<p class="exp">
$$a_\parallel = k$$
$$a_\parallel = k$$
</p>
</p>
<p>In the transverse direction, the acceleration $a_\perp$ is a consequence of the centrifugal force</p>
<p>In the transverse direction, the acceleration $a_\perp$ is a consequence of the centrifugal force</p>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
