To stop a car, first you require a certain reaction time to...

To stop a car, first you require a certain reaction time to begin braking: then the car slows at a constant rate. Suppose that the total distance moved by your car during these two phases is $56.7 \mathrm{~m}$ when its initial speed is $80.5 \mathrm{~km} / \mathrm{h},$ and $24.4 \mathrm{~m}$ when its initial specd is $48.3 \mathrm{~km} / \mathrm{h}$. What are (a) your reaction time and (b) the magnitude of the acceleration?

Key Concepts

Unit Conversion

Unit conversion is important when working with measurements that are given in different units. For example, converting speed from kilometers per hour to meters per second is essential to ensure consistency in calculations when applying kinematic equations in the International System of Units (SI).

Kinematic Equations

Kinematic equations are mathematical formulas that describe the motion of objects under constant acceleration. These equations link variables such as displacement, initial velocity, time, and acceleration. In the context of braking, they are used to model the car’s deceleration phase to compute factors like stopping distance and acceleration magnitude.

Uniform Acceleration

Uniform acceleration (or in this case, uniform deceleration) refers to a constant rate of change of velocity during a given period. When brakes are applied, assuming the deceleration is constant allows for the use of standard kinematic equations to relate the initial speed, the deceleration rate, and the distance covered during the braking phase.

Reaction Time

Reaction time is the interval between the moment a stimulus (such as a need to brake) is perceived and the beginning of the physical response (such as applying the brakes). This concept is crucial in understanding stopping distances because the car continues to move at the initial speed during this delay, contributing to the overall distance traveled before it starts decelerating.

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