Skip to main content
Ch 03: Motion in Two or Three Dimensions
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Young & Freedman Calc 14th EditionCh 03: Motion in Two or Three Dimensions문제 4b
3장, 문제 4b

The position of a squirrel running in a park is given by r⃗=[(0.280 m/s)t+(0.0360 m/s2)t2]i^+(0.0190 m/s3)t3j^\(\vec{r}\) = \(\left\)[ (0.280~\(\mathrm{m/s}\))t + (0.0360~\(\mathrm{m/s^2}\))t^2 \(\right\)] \(\hat{i}\) + (0.0190~\(\mathrm{m/s^3}\))t^3 \(\hat{j}\) . At t=5.00st = 5.00 s, how far is the squirrel from its initial position?

검증된 단계별 안내
1
Identify the position function given: \( \mathbf{r}(t) = [(0.280 \text{ m/s})t + (0.0360 \text{ m/s}^2)t^2]\hat{\mathbf{i}} + (0.0190 \text{ m/s}^3)t^3\hat{\mathbf{j}} \). This function describes the position of the squirrel in terms of time \( t \).
To find the position of the squirrel at \( t = 5.00 \text{ s} \), substitute \( t = 5.00 \text{ s} \) into the position function \( \mathbf{r}(t) \). Calculate each component separately: \( \hat{\mathbf{i}} \) and \( \hat{\mathbf{j}} \).
For the \( \hat{\mathbf{i}} \) component, substitute \( t = 5.00 \text{ s} \) into \( (0.280 \text{ m/s})t + (0.0360 \text{ m/s}^2)t^2 \) and compute the value.
For the \( \hat{\mathbf{j}} \) component, substitute \( t = 5.00 \text{ s} \) into \( (0.0190 \text{ m/s}^3)t^3 \) and compute the value.
Combine the computed \( \hat{\mathbf{i}} \) and \( \hat{\mathbf{j}} \) components to find the position vector \( \mathbf{r}(5.00 \text{ s}) \). The magnitude of this vector will give the distance from the initial position at \( t = 0 \text{ s} \). Use the formula \( \sqrt{(\text{component } \hat{\mathbf{i}})^2 + (\text{component } \hat{\mathbf{j}})^2} \) to find the distance.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
4m
도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Position Vector

The position vector describes the location of an object in space relative to a reference point, often the origin. In this problem, the position vector r is given as a function of time, with components in the î and ĵ directions, representing the squirrel's position in a two-dimensional plane.
추천 영상:
가이드 코스
07:07
Final Position Vector

Displacement

Displacement is the vector quantity that represents the change in position of an object. It is calculated by finding the difference between the final and initial position vectors. In this problem, the displacement at t = 5.00 s is determined by evaluating the position vector at this time and subtracting the initial position.
추천 영상:
가이드 코스
06:13
Displacement vs. Distance

Vector Addition

Vector addition involves combining vectors by adding their corresponding components. To find the squirrel's displacement, the components of the position vector at t = 5.00 s are added algebraically. This process involves summing the individual î and ĵ components to determine the total displacement vector.
추천 영상:
가이드 코스
07:30
Vector Addition By Components
관련 실천
교과서 질문

The position of a squirrel running in a park is given by r⃗=[(0.280 m/s)t+(0.0360 m/s2)t2]i^+(0.0190 m/s3)t3j^\(\vec{r}\) = \(\left\)[ (0.280~\(\mathrm{m/s}\))t + (0.0360~\(\mathrm{m/s^2}\))t^2 \(\right\)] \(\hat{i}\) + (0.0190~\(\mathrm{m/s^3}\))t^3 \(\hat{j}\) . (a) What are vx(t)v_{x}\(\left\)(t\(\right\)) and vy(t)v_{y}\(\left\)(t\(\right\)), the xx-and yy-components of the velocity of the squirrel, as functions of time?

325
views
교과서 질문

A web page designer creates an animation in which a dot on a computer screen has position r→=[4.0cm+(2.5 cm/s2)t2]i+(5.0cm/s)tj\(\overrightarrow{r}\)=\(\left\]\lbrack\)4.0\(\operatorname{cm}\)+\(\left\)(2.5\(\text{ cm/s}\)^2\(\right\))t^2\(\right\[\rbrack\]\mathbf{i}\)+\(\left\)(5.0\(\operatorname{\text{cm/s}\)}\(\right\))t\(\mathbf{j}\). Find the magnitude and direction of the dot's average velocity between t=0t = 0 and t=2.0st=2.0s.

461
views
교과서 질문

The coordinates of a bird flying in the xy-plane are given by x(t) = αt and y(t) = 3.0 m − βt2, where α = 2.4 m/s and β = 1.2 m/s2. (a) Sketch the path of the bird between t = 0 and t = 2.0 s.

2522
views
교과서 질문

The coordinates of a bird flying in the xy-plane are given by x(t) = αt and y(t) = 3.0 m − βt2, where α = 2.4 m/s and β = 1.2 m/s2. Calculate the velocity and acceleration vectors of the bird as functions of time.

307
views
교과서 질문

A dog running in an open field has components of velocity vx = 2.6 m/s and vy = −1.8 m/s at t1 = 10.0 s. For the time interval from t1 = 10.0 s to t2 = 20.0 s, the average acceleration of the dog has magnitude 0.45 m/s2 and direction 31.0° measured from the +x–axis toward the +y–axis. At t2 = 20.0 s, what are the x- and y-components of the dog's velocity?

4165
views