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 47

2장, 문제 47

You are driving to the grocery store at 20 m/s. You are 110 m from an intersection when the traffic light turns red. Assume that your reaction time is 0.50 s and that your car brakes with constant acceleration. What magnitude braking acceleration will bring you to a stop exactly at the intersection?

검증된 단계별 안내

Determine the distance traveled during the reaction time. Use the formula for distance traveled at constant velocity:

d = v t

, where

v

is the velocity (20 m/s) and

t

is the reaction time (0.50 s).

Subtract the distance traveled during the reaction time from the total distance to the intersection to find the distance over which the car must decelerate. Use the formula:

d = d total - d reaction

, where

d total

is 110 m.

Use the kinematic equation to relate the remaining distance, initial velocity, final velocity, and acceleration:

d = v i t + \frac{1}{2} a t^{2}

. Here,

v i

is the initial velocity (20 m/s),

v f

is the final velocity (0 m/s), and

d

is the remaining distance.

Rearrange the kinematic equation to solve for the acceleration

a

. Use the formula:

a = \frac{- v^{i 2}}{2 d}

, where

d

is the remaining distance and

v i

is the initial velocity.

Substitute the known values into the formula for acceleration and simplify to find the magnitude of the braking acceleration. Remember to take the absolute value of the result since the problem asks for the magnitude.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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 car's motion as it approaches the intersection and to calculate the necessary braking distance.

Acceleration

Acceleration is defined as the rate of change of velocity of an object over time. It can be positive (speeding up) or negative (slowing down, also known as deceleration). In this problem, the braking acceleration is crucial to determine how quickly the car can stop before reaching the intersection, given the initial speed and the distance to the stop.

Reaction Time

Reaction time is the delay between the perception of a stimulus and the initiation of a response. In driving scenarios, it affects how quickly a driver can respond to changes, such as a traffic light turning red. In this question, the 0.50 s reaction time must be accounted for when calculating the total distance traveled before the brakes are applied, impacting the required braking acceleration.