A particle moving along the x-axis has its position described by the function x = (2t3 + 2t + 1) m, where t is in s. At t = 2s, what are the particle's position?

Ch 02: Kinematics in One Dimension

Knight Calc - Physics for Scientists and Engineers 5th Edition

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Knight Calc 5th Edition

Ch 02: Kinematics in One Dimension

문제 33a

2장, 문제 33a

A particle moving along the x-axis has its position described by the function x = (2t³ + 2t + 1) m, where t is in s. At t = 2s, what are the particle's position?

검증된 단계별 안내

Step 1: Identify the given position function of the particle, which is x(t) = 2t^3 + 2t + 1 (in meters), where t is in seconds.

Step 2: To find the position of the particle at t = 2s, substitute t = 2 into the position function x(t). This means you will calculate x(2) = 2(2)^3 + 2(2) + 1.

Step 3: Simplify the expression by evaluating the powers and performing the arithmetic operations. Start with the cubic term, then the linear term, and finally add the constant term.

Step 4: After simplifying, the result will give you the position of the particle in meters at t = 2s.

Step 5: Ensure the units are consistent and the final position is expressed in meters, as the problem specifies the position in meters.

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주요 개념

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

Position Function

The position function describes the location of a particle along a specific axis as a function of time. In this case, the position is given by the equation x = (2t^3 + 2t + 1) m, where 't' represents time in seconds. Understanding this function is crucial for determining the particle's position at any given time.

Evaluating Functions

Evaluating a function involves substituting a specific value for the variable to find the corresponding output. For the position function x(t), substituting t = 2 seconds allows us to calculate the exact position of the particle at that moment. This process is fundamental in physics for analyzing motion.

Kinematics

Kinematics is the branch of physics that deals with the motion of objects without considering the forces that cause the motion. It involves concepts such as position, velocity, and acceleration. In this question, understanding kinematics helps in interpreting the position function and its implications for the particle's movement along the x-axis.