A sprinter practicing for the 200 -m dash accelerates...

A sprinter practicing for the 200 -m dash accelerates uniformly from rest at $A$ and reaches a top speed of $40 \mathrm{km} / \mathrm{h}$ at the $60-\mathrm{m}$ mark. He then main tains this speed for the next 70 meters before uniformly slowing to a final speed of $35 \mathrm{km} / \mathrm{h}$ at the finish line. Determine the maximum horizontal acceleration which the sprinter experiences during the run. Where does this maximum acceleration value occur?

A sprinter practicing for the 200 -m dash accelerates uniformly from rest at $A$ and reaches a top speed of $40 \mathrm{km} / \mathrm{h}$ at the $60-\mathrm{m}$ mark. He then main tains this speed for the next 70 meters before uniformly slowing to a final speed of $35 \mathrm{km} / \mathrm{h}$ at the finish line. Determine the maximum horizontal
acceleration which the sprinter experiences during the run. Where does this maximum acceleration value occur?

Key Concepts

Uniform Acceleration

Uniform acceleration refers to motion where the acceleration remains constant throughout a given time interval. This concept is key for determining how speed changes with time and distance in scenarios where the rate of change of velocity does not vary, allowing the use of specific equations that relate initial and final velocities, acceleration, time, and displacement.

Kinematic Equations

Kinematic equations are mathematical formulas used to describe the motion of objects under constant acceleration. These equations, such as v² = u² + 2as, allow for the calculation of acceleration, displacement, velocity, and time, by relating these quantities without needing to explicitly know the time interval of the motion.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another set of units. In problems involving motion, it is often necessary to convert speeds from kilometers per hour to meters per second to ensure consistency with the displacement units, facilitating accurate calculations using physical formulas.

Motion Phases

Motion phases in a problem describe different intervals in the movement of an object, such as periods of acceleration and deceleration. Analyzing distinct phases allows for the identification of the section in which maximum acceleration occurs, typically the phase where the object is speeding up from rest or a lower speed to a higher speed.

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