Chapter 1. calc_tutorial_13_5_033

1.1 Problem Statement

{4,6,8,10}
$a-2
$a-1
pow($a,2)+pow($b,2)+pow($c,2)
round(pow($d,0.5),2)
pow($a,2)
pow($c,2)
{0}
round($a/$e,2)
round($b/$e,2)
round($c/$e,2)
pow($a,3)
pow($c,3)
$l-$m
round($n/pow($d,0.5),2)
round(pow(pow($a,4)+pow($c,4),0.5),2)
round(pow(pow($a,4)+pow($c,4)-$n*$n/$d,0.5),2)

Find the coefficients aT and aN at the specified value of t.

1.2 Step 1

Question Sequence

Question 1.1

Recall how to find the coefficient of the tangential component of acceleration aT and the coefficient of the normal component of acceleration aN.

In the decomposition of the acceleration vector as a sum of its tangential and normal components, a = aTT + aNN, we have

Thus we will need to find a(t) and T(t) at t = 0.

Find a(0) by differentiating twice and evaluating at t = 0.

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

cT/5EWsSl/GiC3EtNVwd2C/FugaZE9nXzMjov2+dAfMN9igXVgHM9FmmfM/ulCrS3f+Y1YavLJ+YuV9xC4mmyimkRkre18YLKxaC8CR2RZQecjiT14c34X6YETm5u6+VYMt1lVELRZGsVZwAK2mWGReCO5hw/JNq3l/d8br0PTYjXPFRLoOAIw8kZp7YQf6k5k05p7USDT4yCHc67hUZA6YSrTWU+3pqQLOT3vLdsm+sTc2HWkQpoZ90sDdixao7dF5DByiLf5dZ/VDs/D+86T7XQDgd0FnZKlgESRsoDr6qEYyM4M7IFV2PCO+wGbznRT2jA+g3HJPJWivAkLxXa0+inGCDjQ5XWSNAq+tmZHTRi1N5UsVRdvUOsc7MXgARYoL4JfBoY7PpqtlcipHWbg8d2sX/K/4cNGWHDKLWuZeqoVPA3AepB4vam3gAi/qi6TBW/hWJx/G3LtqvDFi107o7XZiQ0Br7VtmSWlEUztg4d5VwU0xd/PwgpncDRrCDPoqlLS40NdmSVG4ssRq7deQ1soo87Hx00/g5uckMbI0u4f4BVjMDDRrhiE1SnnUMA7CxN6mA8krkMHEjBG57xyTwzI0YDIdXio7euCsiYMQn9waF3e9tIhxbFn5OokWfTWC/oWXsQGSBA1hbT3eZZu473ANOw63PgGkTVGbDtaDOXOsswwc4UEAVxjn9MEXX92TcFKkTThvhNqRGh2z1su6gRb6O3dIHc05ISbV+omuysmqTrNcEd066SDuaEbqb3aXe9KI2DLTSc/skKWivV2yY8HcqPwMP6IwILvzjgyfFnTw7Pd5hu7kjLUl2rPb4DOvJkF4fWrPx1282LlIn69LN0DVNXLaYfYrzpAhz965rtUf4Mghu2i8W+AMR5Er2Jw8yOmNJ4NeB/8et+JMSW0792zS+5j0Nh1htELXKPYNaBEJu2wFtQNHq3tJHD6gmaz/ZoUXr5oOVabNnowwh19UoeSxJYn/0boEct+Hzt87LzCjLViu5HAK8VL0p9i7hgOPR5xLFAsPw9b/xh4YXls5tcf+eNVdlx6GTUBkR9DpKWI3a554Tt0F980WjhqZwRe/+DSpYwhl4shXLLFeg4i+q1U9VVTuQUVkpcRF+eak5tv0eNKhy9ypIdfyNaU4ykGV3ZtbriaPF8SFqyYIZm3KDo0WtbU1FfjMkpzIWdGxUj/kmy3q4bBBotqMJGKXsQSc0QOG6a7SkdKcv52ul0TOPwdyQ2F1Iczk0dDZ2TdH2aAEuXY0fdfsn4OYXui84oj2G+lXTaw8sMkuYfQ+f5MZ+RSeMwEYADLmuKZNF0hT4yUu9tRmvLoO009L5t4QBSHIrDA==

a(0) = <or6dmYWrEbA=, Hs0oCnDH0eo=, mpgA8Zi4UKU=>

Correct.
Incorrect.

1.3 Step 2

Question Sequence

Question 1.2

Find the unit tangent vector, T(0), by evaluating r'(0) and ||r'(0)||. Round your answers to two decimal places.

r'(0) = <nc1ItEz0kR4=, iSba6t70dtA=, YWSdEbNFjeo=>

||r'(0)|| = 5dWJhLEUU4Y=

= <zDsgB75cNfg=, bEz/iYnXpnk=, EDRjY19slEE=>

Correct.
Incorrect.

1.4 Step 3

Question Sequence

Question 1.3

Find aT at t = 0. Round your answer to two decimal places.

aT = a(0) ⋅ T(0)

= fhf0phNsVCo=

Correct.
Incorrect.

1.5 Step 4

Question Sequence

Question 1.4

In order to find , we need to compute ||a|| at t = 0.

Find ||a|| at t = 0. Round your answers to two decimal places.

a(0) = <$f, 0, $g>

||a(0)|| = 3jRAm4T6Mr4=

Find aN at t = 0.

= VdD/yKVKNAI=

Correct.
Incorrect.