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 15th Edition

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Young & Freedman Calc 15th Edition

Ch 02: Motion Along a Straight Line

Problem 20a

Chapter 2, Problem 20a

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.

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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 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.

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Unit Conversions

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