Chapter 1. calc_tutorial_13_5_017

1.1 Problem Statement

{3,5,7,8}
{2,4,6,9}
round(pow($a,2)/2,2)
round(pow($b,2)/2,2)
$c+$d

Find r(t) and v(t) given a(t) and the initial velocity and position.

a(t) = tk, v(0) = 8i, r(0) = 6j

1.2 Step 1

Question Sequence

Question 1.1

Given a(t), recall how to find the velocity and position vectors.

Using a(t) = tk, find v(t).

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
Correct.
Incorrect.

1.3 Step 2

Question Sequence

Question 1.2

Substitute the initial condition, v(0) = $ai, to solve for v0.

v0 = nc1ItEz0kR4=i

Thus,

v(t) =

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
Correct.
Incorrect.

1.4 Step 3

Question Sequence

Question 1.3

Using v(t) found in Step 2, find r(t).

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
Correct.
Incorrect.

1.5 Step 4

Question Sequence

Question 1.4

Substitute the initial condition, r(0) = $bj, to solve for r0.

r0 = iSba6t70dtA=j

Thus,

r(t) =

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
Correct.
Incorrect.