A car sits on an entrance ramp to a freeway, waiting for a break in the traffic. Then the driver accelerates with constant acceleration along the ramp and onto the freeway. The car starts from rest, moves in a straight line, and has a speed of $20$ m/s ( $45$ mi/h) when it reaches the end of the $120$ -m-long ramp. What is the acceleration of the car?

검증된 단계별 안내

Identify the known values: initial velocity (v₀) = 0 m/s (since the car starts from rest), final velocity (v) = 20 m/s, and displacement (s) = 120 m.

Use the kinematic equation that relates these quantities: v² = v₀² + 2as, where v is the final velocity, v₀ is the initial velocity, a is the acceleration, and s is the displacement.

Substitute the known values into the equation: (20 m/s)² = (0 m/s)² + 2a(120 m).

Simplify the equation to solve for acceleration (a): 400 m²/s² = 240a m.

Rearrange the equation to isolate a: a = 400 m²/s² / 240 m.

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주요 개념

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Kinematics Equations

Kinematics equations describe the motion of objects without considering the forces that cause the motion. For constant acceleration, the equation v^2 = u^2 + 2as can be used, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement. This equation helps determine the car's acceleration given its initial and final velocities and the distance traveled.

Constant Acceleration

Constant acceleration implies that the rate of change of velocity is uniform over time. In this scenario, the car's acceleration remains the same throughout its motion on the ramp. Understanding constant acceleration is crucial for applying kinematic equations correctly, as it simplifies calculations by allowing the use of specific formulas designed for uniform acceleration.

Initial Conditions

Initial conditions refer to the state of an object at the beginning of its motion. Here, the car starts from rest, meaning its initial velocity is zero. Recognizing initial conditions is essential for solving physics problems, as they provide the necessary starting point for applying kinematic equations and determining other variables like acceleration or time.