Ch 02: Motion Along a Straight Line

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

Young & Freedman Calc 15th 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.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

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.

Recommended video:

Guided course

7:27

Escape Velocity

Related Practice

Textbook Question

An antelope moving with constant acceleration covers the distance between two points $70.0$ m apart in $6.00$ s. Its speed as it passes the second point is $15.0$ m/s. What is its acceleration?

views

Textbook Question

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. How much time does it take the car to travel the length of the ramp?

views

Textbook Question

An astronaut has left the International Space Station to test a new space scooter. Her partner measures the following velocity changes, each taking place in a $10$ -s interval. What are the magnitude, the algebraic sign, and the direction of the average acceleration in each interval? Assume that the positive direction is to the right.

(a) At the beginning of the interval, the astronaut is moving toward the right along the $x$ -axis at $15.0$ m/s, and at the end of the interval she is moving toward the right at $5.0$ m/s.

(b) At the beginning she is moving toward the left at $5.0$ m/s, and at the end she is moving toward the left at $15.0$ m/s.

(c) At the beginning she is moving toward the right at $15.0$ m/s, and at the end she is moving toward the left at $15.0$ m/s.

In the fastest measured tennis serve, the ball left the racquet at $73.14$ m/s. A served tennis ball is typically in contact with the racquet for $30.0$ ms and starts from rest. Assume constant acceleration. What was the ball's acceleration during this serve?

views

Textbook Question

The human body can survive an acceleration trauma incident (sudden stop) if the magnitude of the acceleration is less than $250$ m/s². If you are in an automobile accident with an initial speed of $105$ km/h ( $65$ mi/h) and are stopped by an airbag that inflates from the dashboard, over what distance must the airbag stop you for you to survive the crash?

views

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?