In the fastest measured tennis serve, the ball left the racquet at 73.1473.14 m/s. A served tennis ball is typically in contact with the racquet for 30.030.0 ms and starts from rest. Assume constant acceleration. What was the ball's acceleration during this serve?

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

All textbooks

Young & Freedman Calc 14th Edition

Ch 02: Motion Along a Straight Line

Problem 22a

Chapter 2, Problem 22a

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?

Verified step by step guidance

Identify the known values: initial velocity (v₀) = 0 m/s (since the ball starts from rest), final velocity (v) = 73.14 m/s, and time (t) = 30.0 ms = 0.030 s.

Use the formula for acceleration under constant acceleration: a = (v - v₀) / t.

Substitute the known values into the formula: a = (73.14 m/s - 0 m/s) / 0.030 s.

Simplify the expression to find the acceleration: a = 73.14 m/s / 0.030 s.

The result from the simplification will give you the acceleration of the ball during the serve.

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 under constant acceleration. They relate displacement, initial velocity, final velocity, acceleration, and time. In this problem, the equation v = u + at is crucial, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Constant Acceleration

Constant acceleration means that the rate of change of velocity is uniform over time. This simplifies calculations as the acceleration value remains the same throughout the motion. In this scenario, the ball's acceleration is constant while in contact with the racquet, allowing us to use kinematic equations effectively.

Unit Conversion

Unit conversion is essential for ensuring consistency in calculations. In this problem, time is given in milliseconds, which must be converted to seconds (1 ms = 0.001 s) to match the standard SI units used in kinematic equations. This ensures accurate computation of acceleration.

Recommended video:

Guided course

07:46

Unit Conversions

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's velocity as a function of time is given by $v_x(t) = α + βt^2$ , where $α = 3.00$ m/s and $β = 0.100$ m/s³. Draw $v_{x}$ - $t$ and $a_{x}$ - $t$ graphs for the car's motion between $t equals 0$ and $t equals 5.00$ s.

views

Textbook Question

A pilot who accelerates at more than $4 g$ begins to 'gray out' but doesn't completely lose consciousness. Assuming constant acceleration, what is the shortest time that a jet pilot starting from rest can take to reach Mach $4$ (four times the speed of sound) without graying out? (Use $331$ m/s for the speed of sound in cold air.)

views

rank

Textbook Question

A pilot who accelerates at more than $4 g$ begins to 'gray out' but doesn't completely lose consciousness. How far would the plane travel during this period of acceleration? (Use $331$ m/s for the speed of sound in cold air.)

views

Textbook Question

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?

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