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Ch. 02 - Describing Motion: Kinematics in One Dimension
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179당신이 사용하는 게 아니라요?교과서 변경
2장, 문제 41c

A car traveling 85 km/h slows down at a constant 0.50 m/s² just by 'letting up on the gas.' Calculate the distance it travels during the first and fifth seconds.

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1
Convert the car's initial velocity from km/h to m/s. Use the conversion factor: 1 km/h = 0.27778 m/s. The formula is: \( v_0 = 85 \times 0.27778 \).
Use the kinematic equation \( x = v_0 t + \frac{1}{2} a t^2 \) to calculate the distance traveled during the first second. Here, \( v_0 \) is the initial velocity, \( a \) is the acceleration (-0.50 m/s²), and \( t \) is the time (1 second).
To find the distance traveled during the fifth second, calculate the total distance traveled in 5 seconds using the same kinematic equation \( x = v_0 t + \frac{1}{2} a t^2 \). Then, calculate the total distance traveled in 4 seconds using the same equation. Subtract the distance traveled in 4 seconds from the distance traveled in 5 seconds to get the distance traveled during the fifth second.
Substitute the known values into the equations: \( v_0 \) (converted from step 1), \( a = -0.50 \ \text{m/s}^2 \), and \( t \) (1 second for the first second, and 5 seconds for the fifth second).
Simplify the expressions to find the distances for the first and fifth seconds. Remember to keep track of units and signs (negative acceleration indicates slowing down).

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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, acceleration, and time. In this problem, understanding kinematic equations is essential to calculate the distance traveled by the car during specific time intervals.
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Kinematics Equations

Acceleration

Acceleration is defined as the rate of change of velocity of an object with respect to time. It can be positive (speeding up) or negative (slowing down), as in this case where the car decelerates at a constant rate of 0.50 m/s². This concept is crucial for determining how the car's speed changes over time and affects the distance traveled.
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Intro to Acceleration

Equations of Motion

The equations of motion describe the relationship between an object's displacement, initial velocity, acceleration, and time. For uniformly accelerated motion, the equation s = ut + 0.5at² can be used, where s is the distance, u is the initial velocity, a is the acceleration, and t is the time. These equations are vital for calculating the distance the car travels during the specified seconds.
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Equations of Rotational Motion