Acceleration A drag racer accelerates at a(t)=88 ft/s². Assume v(0)=0, s(0)=0, and t is measured in seconds.

d. How long does it take the racer to travel 300 ft?

검증된 단계별 안내

Identify the given acceleration function: \(a(t) = 88\) ft/s², which is constant.

Since acceleration is the derivative of velocity, integrate \(a(t)\) with respect to \(t\) to find the velocity function: \(v(t) = \int a(t) \, dt = \int 88 \, dt\).

Use the initial condition \(v(0) = 0\) to solve for the constant of integration in the velocity function.

Next, integrate the velocity function \(v(t)\) with respect to \(t\) to find the position function \(s(t)\): \(s(t) = \int v(t) \, dt\).

Use the initial condition \(s(0) = 0\) to solve for the constant of integration in the position function, then set \(s(t) = 300\) ft and solve for \(t\) to find the time it takes to travel 300 ft.

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.

Acceleration and Its Relationship to Velocity and Position

Acceleration is the rate of change of velocity with respect to time. Given acceleration a(t), velocity v(t) can be found by integrating a(t). Similarly, position s(t) is found by integrating velocity. Understanding these relationships allows us to move from acceleration to position over time.

Initial Conditions in Integration

Initial conditions such as v(0) = 0 and s(0) = 0 provide specific values needed to solve the constants of integration when finding velocity and position functions. These conditions ensure the solution matches the physical scenario described.

Solving for Time from Position Function

Once the position function s(t) is determined, solving for the time t when s(t) equals a given distance (300 ft) involves algebraic manipulation. This step finds the exact time required for the racer to travel the specified distance.

Acceleration A drag racer accelerates at a(t)=88 ft/s². Assume v(0)=0, s(0)=0, and t is measured in seconds.d. How long does it take the racer to travel 300 ft?