Chapter 1. calc_tutorial_13_3_010

1.1 Problem Statement

{2,3,5,7,9}
{9,25,26,27,28,29,36}
pow($a,2)+1
round(pow($c,0.5)/$a ,3)

Find the speed at the given value of t.

1.2 Step 1

Question Sequence

Question 1.1

Suppose a particle moves along a vector-valued path function, r(t) = <x(t), y(t), z(t)>. Then we define v(t) = r'(t) as the velocity of the particle as it moves along the path, and we define the speed of the particle as the magnitude of the velocity vector. We denote speed by v(t) = ||r'(t)||.

Find v(t) = r'(t), the velocity vector.

v(t) =

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
Correct.
Incorrect.

1.3 Step 2

Question Sequence

Question 1.2

Find the velocity vector of the particle at t = $a.

v($a) = r'($a) =

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
Correct.
Incorrect.

1.4 Step 3

Question Sequence

Question 1.3

Find the speed of the particle at t = $a. Round your answer to three decimal places.

v($a) = ||r'($a)|| = U2GIbglD1oM=

Correct.
Incorrect.