Car A is traveling at 25 mi / hr and applies the brakes at the position shown so as to arrive at

step 1 In this question it is told that a body starts from the rest and it has a velocity versus time r

Car A is traveling at 25 mi / hr and applies the brakes at...

Car $A$ is traveling at $25 \mathrm{mi} / \mathrm{hr}$ and applies the brakes at the position shown so as to arrive at the intersection $C$ at a complete stop with a constant deceleration. Car $B$ has a speed of $40 \mathrm{mi} / \mathrm{hr}$ at the instant represented and is capable of a maximum deceleration of $18 \mathrm{ft} / \mathrm{sec}^{2} .$ If the driver of $\operatorname{car} B$ is distracted, and does not apply his brakes until 1.30 seconds after car $A$ begins to brake, the result being a collision with car $A$, with what relative speed will car $B$ strike car $A ?$ Treat both cars as particles.

Key Concepts

Uniformly Accelerated Motion

This concept involves the analysis of objects moving with a constant acceleration (or deceleration, which is simply negative acceleration). The equations of motion under uniform acceleration allow one to relate displacement, initial velocity, time, and acceleration. It is fundamental for solving problems relating to braking distances, stopping times, and collision outcomes in scenarios where the acceleration does not change over time.

Reaction Time and Delayed Braking

Reaction time refers to the delay between the decision to act (such as applying brakes) and the actual application of that action. In kinematics, this delay is critical because a vehicle continues at its initial speed during the reaction interval, thereby covering additional distance before deceleration begins. Understanding how reaction delays impact overall motion is essential in accurately predicting positions and velocities at specific moments.

Relative Velocity

Relative velocity is the measure of the velocity of one object as observed from another object's frame of reference. In collision analysis, it is crucial to calculate the difference in speeds between two objects immediately before impact, as this relative speed determines the severity of the collision and the dynamics of the interaction.

Unit Conversion

Many kinematics problems require the conversion of units to maintain consistency, particularly when different quantities are provided in different units (for example, converting miles per hour to feet per second). Proper unit conversion ensures that all terms in the equations are compatible, leading to accurate results in calculations of speed, distance, and acceleration.

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