Chapter 11: Q. 9 (page 901)

Velocity and acceleration vectors: Find the velocity and acceleration vectors for the given vector functions.
$r (t) = ⟨ t, 2 t - 3, 3 t + 5 ⟩$

Short Answer

Expert verified

Ans: $v (t) = ⟨ 1, 2, 3 ⟩ and a (t) = ⟨ 0, 0, 0 ⟩$

Step by step solution

Step 1. Given information:

$r (t) = ⟨ t, 2 t - 3, 3 t + 5 ⟩$

Step 2. Denoting the velocity and acceleration of the vector:

The velocity vector, $v (t)$ is given by

$v (t) = \frac{d}{d t} r (t) = <\frac{d}{d t} x (t), \frac{d}{d t} y (t), \frac{d}{d t} z (t)>$ .

That is , we take the derivative of each component function of $r (t)$ .

The acceleration vector, $a (t)$ is given by

$a (t) = \frac{d}{d t} v (t)$ . That is, $a (t)$ is obtained by taking the derivative of each component function of $v (t)$ .

Step 3. Finding the velocity and acceleration of the vector:

Consider $r (t) = ⟨ t, 2 t - 3, 3 t + 5 ⟩$

localid="1649657595879" $v (t) = \frac{d}{d t} (r (t)) = \frac{d}{d t} ⟨ t, 2 t - 3, 3 t + 5 ⟩ = <\frac{d}{d t} (t), \frac{d}{d t} (2 t - 3), \frac{d}{d t} (3 t + 5)> = ⟨ 1, 2, 3 ⟩ a (t) = \frac{d}{d t} (v (t)) = \frac{d}{d t} ⟨ 1, 2, 3 ⟩ = <\frac{d}{d t} (1), \frac{d}{d t} (2), \frac{d}{d t} (3)> = ⟨ 0, 0, 0 ⟩$

thus

$v (t) = ⟨ 1, 2, 3 ⟩ and a (t) = ⟨ 0, 0, 0 ⟩$

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Velocity and acceleration vectors: Find the velocity and acceleration vectors for the given vector functions.
$r (t) = ⟨ t, 2 t - 3, 3 t + 5 ⟩$

Short Answer

Step by step solution

Step 1. Given information:

Step 2. Denoting the velocity and acceleration of the vector:

Step 3. Finding the velocity and acceleration of the vector:

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Velocity and acceleration vectors: Find the velocity and acceleration vectors for the given vector functions.r(t)=⟨t,2t-3,3t+5⟩

Short Answer

Step by step solution

Step 1. Given information:

Step 2. Denoting the velocity and acceleration of the vector:

Step 3. Finding the velocity and acceleration of the vector:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Study anywhere. Anytime. Across all devices.

Velocity and acceleration vectors: Find the velocity and acceleration vectors for the given vector functions.
$r (t) = ⟨ t, 2 t - 3, 3 t + 5 ⟩$