A well-thrown ball is caught in a well-padded mitt. If the...

A well-thrown ball is caught in a well-padded mitt. If the deceleration of the ball is $2.10 \times 10^{4} \mathrm{m} / \mathrm{s}^{2},$ and 1.85 $\mathrm{ms}$ $\left(1 \mathrm{ms}=10^{-3} \mathrm{s}\right)$ elapses from the time the ball first touches the mitt until it stops, what was the initial velocity of the ball?

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Key Concepts

Time Interval

The time interval over which acceleration occurs is a crucial factor in kinematic problems. It is used to quantify how long a force has acted to change the velocity of an object, and its accurate measurement and conversion to consistent units are necessary for correctly solving motion equations.

Unit Conversion

In physics, ensuring that all quantities are in compatible units is essential for accurate calculations. Converting units, such as milliseconds to seconds, allows the correct application of formulas and helps maintain consistency across different parts of a problem.

Constant Acceleration

This concept involves motion where acceleration remains uniform over time. It is fundamental in kinematics and allows the use of standard equations to relate displacement, time, initial velocity, and final velocity. Applying these equations simplifies the analysis of motion problems where forces cause a steady increase or decrease in speed.

Deceleration

Deceleration refers to a decrease in the speed of an object, which is essentially negative acceleration. Understanding deceleration as a specific case of constant acceleration is important because it allows the same kinematics principles to be applied, with careful attention to the sign of the acceleration value.

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