On a dry road, a car with good tires may be able to brake...

On a dry road, a car with good tires may be able to brake with a constant decclcration of $4.92 \mathrm{~m} / \mathrm{s}^{2}$. (a) How long docs such a car, initially traveling at $24.6 \mathrm{~m} / \mathrm{s}$, take to stop? (b) How far does it travel in this time? (c) Graph $x$ versus $t$ and $v$ versus $t$ for the deceleration.

On a dry road, a car with good tires may be able to brake with a constant decclcration of $4.92 \mathrm{~m} / \mathrm{s}^{2}$. (a) How long docs such a car, initially traveling at $24.6 \mathrm{~m} / \mathrm{s}$, take to stop? (b) How far does it travel in this time?
(c) Graph $x$ versus $t$ and $v$ versus $t$ for the deceleration.

Key Concepts

Uniform Acceleration Kinematics

This concept involves the study of motion where the acceleration remains constant over time. It uses equations that relate displacement, initial velocity, final velocity, acceleration, and time, allowing the analysis of both speeding up and slowing down motions without having to change the acceleration value during the motion.

Deceleration

Deceleration refers to a reduction in speed or a negative acceleration. It is essentially the same as acceleration but in the opposite direction of the motion, and it is used when an object is slowing down. The same kinematic equations apply, but the acceleration has a negative sign when paired with the object’s velocity.

Kinematic Equations

These are a set of mathematical formulas used to predict the motion of objects under constant acceleration. They include equations such as v = u + at for velocity, and s = ut + 0.5at² for displacement, which are crucial for analyzing various parameters of motion like stopping time and distance traveled during deceleration scenarios.

Motion Graphs

Graphing the relationships between position, velocity, and time provides a visual representation of motion. A position versus time graph typically shows a curve where the slope represents velocity, while a velocity versus time graph has a constant slope when acceleration is uniform. These graphs help in understanding and predicting the behavior of moving objects under constant acceleration or deceleration.

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