The brakes on your car can slow you at a rate of 5.2 m / s^2. (a) If you are going 137 km / h

step 1 All right. So we've got A equals negative 5 .2 meters per second square. And V is 137 kilometers

The brakes on your car can slow you at a rate of 5.2 m /...

The brakes on your car can slow you at a rate of $5.2 \mathrm{~m} / \mathrm{s}^{2}$. (a) If you are going $137 \mathrm{~km} / \mathrm{h}$ and suddenly see a state trooper, what is the minimum time in which you can get your car under the $90 \mathrm{~km} / \mathrm{h}$ speed limit? (The answer reveals the futility of braking to keep your high speed from being detected with a radar or laser gun.) (b) Graph $x$ versus $t$ and $v$ versus $t$ for such a slowing.

The brakes on your car can slow you at a rate of $5.2 \mathrm{~m} / \mathrm{s}^{2}$. (a) If you are going $137 \mathrm{~km} / \mathrm{h}$ and suddenly see a state trooper, what is the minimum time in which you can get your car under the $90 \mathrm{~km} / \mathrm{h}$ speed limit? (The answer reveals the futility of braking to keep your high speed from being detected with a radar or laser gun.)
(b) Graph $x$ versus $t$ and $v$ versus $t$ for such a slowing.

Key Concepts

Uniformly Accelerated Motion

This concept refers to the motion of an object when the acceleration remains constant over time. It is fundamental in kinematics and allows the use of standard equations to relate displacement, velocity, acceleration, and time. These equations are essential for solving problems where initial and final velocities, as well as deceleration or acceleration, are known.

Constant Acceleration Equations

These equations, such as v = v? + a*t and x = x? + v?*t + (1/2)*a*t², provide a way to quantitatively analyze motion under uniform acceleration or deceleration conditions. They are used to determine key quantities like the time required to change speed, the distance covered during acceleration, and other related parameters.

Unit Conversion

Converting units, particularly speed units such as from kilometers per hour to meters per second, is a critical step in solving kinematics problems. Correct unit conversion ensures consistency in the calculations and the proper application of physics equations.

Deceleration

Deceleration is the process of reducing speed, characterized by a constant negative acceleration. Understanding deceleration is crucial to solving problems related to braking, as it directly influences the time and distance required to reduce the speed of a moving object.

Graphical Representation of Motion

Graphing motion involves plotting variables such as displacement versus time and velocity versus time. The position-time graph helps visualize how an object's location changes over time, often resulting in a curved line under constant acceleration, while the velocity-time graph is typically linear for uniform acceleration or deceleration, providing a clear picture of the rate at which the velocity changes.

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