Ch 02: Motion Along a Straight Line

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 02: Motion Along a Straight Line

Problem 21a

Chapter 2, Problem 21a

The fastest measured pitched baseball left the pitcher's hand at a speed of $45.0$ m/s. If the pitcher was in contact with the ball over a distance of $1.50$ m and produced constant acceleration, what acceleration did he give the ball?

Verified step by step guidance

Start by identifying the known values: initial velocity (v₀) is 0 m/s (assuming the ball starts from rest), final velocity (v) is 45.0 m/s, and the distance (d) over which the acceleration occurs is 1.50 m.

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

Since the initial velocity v₀ is 0 m/s, the equation simplifies to v² = 2ad.

Rearrange the equation to solve for acceleration (a): a = v² / (2d).

Substitute the known values into the equation: a = (45.0 m/s)² / (2 * 1.50 m). This will give you the acceleration imparted to the ball by the pitcher.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Kinematics Equations

Kinematics equations describe the motion of objects without considering the causes of motion. They relate displacement, initial velocity, final velocity, acceleration, and time. In this problem, the equation v^2 = u^2 + 2as is relevant, where v is the final velocity, u is the initial velocity, a is acceleration, and s is displacement.

Constant Acceleration

Constant acceleration means that the rate of change of velocity is uniform over time. This simplifies calculations as the kinematic equations can be directly applied. In this scenario, the pitcher's acceleration is constant, allowing us to use the kinematic equation to find the acceleration given the initial and final velocities and the displacement.

Initial and Final Velocity

Initial velocity is the speed at which an object starts its motion, while final velocity is the speed at which it ends. In this problem, the initial velocity is 0 m/s (assuming the ball starts from rest), and the final velocity is 45.0 m/s. These values are crucial for calculating the acceleration using the kinematic equations.

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The fastest measured pitched baseball left the pitcher's hand at a speed of 45.045.0 m/s. If the pitcher was in contact with the ball over a distance of 1.501.50 m and produced constant acceleration, what acceleration did he give the ball?

Verified video answer for a similar problem:

Key Concepts

Kinematics Equations

Constant Acceleration

Initial and Final Velocity

The fastest measured pitched baseball left the pitcher's hand at a speed of $45.0$ m/s. If the pitcher was in contact with the ball over a distance of $1.50$ m and produced constant acceleration, what acceleration did he give the ball?