A jet plane is cruising at 300 m/s when suddenly the pilot turns the engines up to full throttle. After traveling 4.0 km, the jet is moving with a speed of 400 m/s. What is the magnitude of the jet's acceleration, assuming it to be a constant acceleration?

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Identify the known quantities: initial velocity \( v_0 = 300 \; \text{m/s} \), final velocity \( v = 400 \; \text{m/s} \), and displacement \( s = 4.0 \; \text{km} = 4000 \; \text{m} \). The goal is to find the constant acceleration \( a \).

Use the kinematic equation that relates velocity, displacement, and acceleration: \( v^2 = v_0^2 + 2as \). Rearrange this equation to solve for \( a \): \( a = \frac{v^2 - v_0^2}{2s} \).

Substitute the known values into the equation: \( a = \frac{(400)^2 - (300)^2}{2 \cdot 4000} \).

Simplify the numerator \( (400)^2 - (300)^2 \) and the denominator \( 2 \cdot 4000 \) to prepare for the calculation of \( a \).

Once simplified, divide the numerator by the denominator to find the magnitude of the acceleration \( a \).

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주요 개념

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

Acceleration

Acceleration is defined as the rate of change of velocity of an object with respect to time. It is a vector quantity, meaning it has both magnitude and direction. In this scenario, the jet's acceleration can be calculated using the change in speed over the distance traveled, assuming constant acceleration.

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. They relate displacement, initial velocity, final velocity, acceleration, and time. In this problem, the relevant kinematic equation can be used to find acceleration by relating the initial and final velocities with the distance traveled.

Velocity

Velocity is the speed of an object in a specified direction and is also a vector quantity. In this case, the initial velocity of the jet is 300 m/s, and the final velocity after traveling 4.0 km is 400 m/s. Understanding the difference between initial and final velocity is crucial for calculating acceleration.