Chapter 11: Q.51 (page 872)

Use the given acceleration vectors $a (t) = v (t) = r (t)$ and initial conditions in Exercises to find the position function $r (t) .$
localid="1650040775983" $a (t) = - 32 j, v (0) = 5 i + 5 j, r (0) = 26 j$

Short Answer

Expert verified

$a (t) = - 32 j, v (0) = 5 i + 5 j, r (0) = 26 j$

$r (t) = 5 ti + 1 (- 16 t^{2} + 5 t + 26) j$

Step by step solution

Given Information

Consider, $a (t) = - 32 j, v (0) = 5 i + 5 j, r (0) = 26 j$

The objective is to find the position function r(t)

since

$a (t) = v^{2} (t) = r^{2} (t), We have v (t) = \int a (t) dt and r (t) = \int v (t) dt now v (t) = \int a (t) dt = \int - 32 jdt v (0) = c_{1} i + c_{2} j . . . . . . . . . . . . (1) v (0) = 5 i + 5 j . . . . . . . . . . . . (2)$

Calculation

Comparing(1) and (2) equations,

$c 1 = 5, c 2 = 5$

so,

$v (t) = 5 i + (- 32 t + 5) j r (t) = \int v (t) d t = \int (5 i + (- 32 i + 5) j) dt$

Where $C$ is a vector constant

$= (5 i + c_{3}) i + (- 16 t^{2} + 5 t + c_{4}) j$

Where $C_{3}$ and $C_{4}$ are scalars

$r (0) = 26 j t h u s, r (t) = 5 t i + 1 (- 16 t^{2} + 5 t + 26) j$

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Use the given acceleration vectors $a (t) = v (t) = r (t)$ and initial conditions in Exercises to find the position function $r (t) .$
localid="1650040775983" $a (t) = - 32 j, v (0) = 5 i + 5 j, r (0) = 26 j$

Short Answer

Step by step solution

Given Information

Calculation

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Use the given acceleration vectors a(t)=v(t)=r(t)and initial conditions in Exercises to find the position function r(t).localid="1650040775983" a(t)=−32j,v(0)=5i+5j,r(0)=26j

Short Answer

Step by step solution

Given Information

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Logic and Functions

Decision Maths

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Use the given acceleration vectors $a (t) = v (t) = r (t)$ and initial conditions in Exercises to find the position function $r (t) .$
localid="1650040775983" $a (t) = - 32 j, v (0) = 5 i + 5 j, r (0) = 26 j$