Careful measurements have been made of Olympic sprinters in...

Careful measurements have been made of Olympic sprinters in the 100-meter dash. A simple but reasonably accurate model is that a sprinter accelerates at $3.6 \mathrm{~m} / \mathrm{s}^2$ for $3 \frac{1}{5} \mathrm{~s}$, then runs at constant velocity to the finish line. a. What is the race time for a sprinter who follows this model? b. A sprinter could run a faster race by accelerating faster at the beginning, thus reaching top speed sooner. If a sprinter's top speed is the same as in part a, what acceleration would he need to run the 100 -meter dash in $9.9 \mathrm{~s}$ ? c. By what percent did the sprinter need to increase his acceleration in order to decrease his time by $1 \%$ ?

Careful measurements have been made of Olympic sprinters in the 100-meter dash. A simple but reasonably accurate model is that a sprinter accelerates at $3.6 \mathrm{~m} / \mathrm{s}^2$ for $3 \frac{1}{5} \mathrm{~s}$, then runs at constant velocity to the finish line.
a. What is the race time for a sprinter who follows this model?
b. A sprinter could run a faster race by accelerating faster at the beginning, thus reaching top speed sooner. If a sprinter's top speed is the same as in part a, what acceleration would he need to run the 100 -meter dash in $9.9 \mathrm{~s}$ ?
c. By what percent did the sprinter need to increase his acceleration in order to decrease his time by $1 \%$ ?

Key Concepts

Percentage Change Calculation

This involves calculating how a physical quantity changes in terms of percent relative to its original value. It is especially useful when evaluating the effect of modifying one parameter, such as acceleration, on the total time or performance outcomes.

Kinematics Equations

These are the mathematical formulas that describe the relationships between displacement, velocity, acceleration, and time in motion. They are essential tools for solving problems involving uniformly accelerated motion as well as segments of constant velocity.

Segmented Motion Analysis

In many real-world motion problems, the overall motion is broken into distinct phases, such as an acceleration phase and a constant velocity phase. Analyzing each segment separately using the appropriate kinematic principles allows for the determination of overall performance metrics like total time or displacement.

Uniformly Accelerated Motion

This concept refers to motion in which an object experiences a constant acceleration. The motion can be analyzed using the kinematics equations, such as s = (1/2)at² and v = at, to determine distances covered and velocities reached during the acceleration period.

Constant Velocity Motion

This concept deals with motion where an object travels at a fixed speed in a given direction, meaning there is no acceleration. The displacement in this phase is simply the product of the constant speed and the time duration.

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