Ch 02: Kinematics in One Dimension

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경

Knight Calc 5th Edition

Ch 02: Kinematics in One Dimension

문제 68a

2장, 문제 68a

David is driving a steady 30 m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady 2.0 m/s² at the instant when David passes. How far does Tina drive before passing David?

검증된 단계별 안내

Define the motion equations for both David and Tina. For David, since he is moving at a constant velocity, his position as a function of time is given by:

x_D = v_D \(\cdot\) t

, where

v_D = 30 \; \(\text{m/s}\)

. For Tina, since she starts from rest and accelerates uniformly, her position as a function of time is given by:

x_T = \(\frac{1}{2}\) a_T \(\cdot\) t^2

, where

a_T = 2.0 \; \(\text{m/s}\)^2

Set the positions of David and Tina equal to each other to find the time

t

when Tina passes David. This gives the equation:

v_D \(\cdot\) t = \(\frac{1}{2}\) a_T \(\cdot\) t^2

Simplify the equation to solve for

t

. Divide through by

t

(assuming

t \(\neq\) 0

v_D = \(\frac{1}{2}\) a_T \(\cdot\) t

. Rearrange to find

t

t = \(\frac{2 \cdot v_D}{a_T}\)

Substitute the known values of

v_D = 30 \; \(\text{m/s}\)

and

a_T = 2.0 \; \(\text{m/s}\)^2

into the equation for

t

to calculate the time it takes for Tina to pass David.

Use the value of

t

to find the distance Tina drives before passing David. Substitute

t

into Tina's position equation:

x_T = \(\frac{1}{2}\) a_T \(\cdot\) t^2

. This will give the distance Tina drives before passing David.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

10m

도움이 되었나요?

주요 개념

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

Kinematics

Kinematics is the branch of mechanics that deals with the motion of objects without considering the forces that cause the motion. It involves concepts such as displacement, velocity, and acceleration. In this scenario, understanding kinematics is essential to analyze the motion of both David and Tina, particularly how their positions change over time.

Equations of Motion

The equations of motion describe the relationship between an object's displacement, initial velocity, acceleration, and time. For Tina, who starts from rest and accelerates, the equation s = ut + 0.5at² is particularly relevant, where 's' is displacement, 'u' is initial velocity, 'a' is acceleration, and 't' is time. This equation will help determine how far Tina travels before she catches up with David.

Relative Motion

Relative motion refers to the calculation of the motion of an object as observed from a particular reference frame. In this problem, David's constant speed and Tina's accelerating motion must be analyzed relative to each other. Understanding relative motion is crucial to determine when and where Tina will pass David, as it involves comparing their positions over time.