Kathy Kool buys a sports car that can accelerate at the rate...

Kathy Kool buys a sports car that can accelerate at the rate of $4.90 \mathrm{m} / \mathrm{s}^{2} .$ She decides to test the car by racing with another speedster, Stan Speedy. Both start from rest, but experienced Stan leaves the starting line 1.00 s before Kathy. If Stan moves with a constant acceleration of $3.50 \mathrm{m} / \mathrm{s}^{2}$ and Kathy maintains an acceleration of $4.90 \mathrm{m} / \mathrm{s}^{2},$ find. (a) the time at which Kathy overtakes Stan, (b) the distance she travels before she catches him, and (c) the speeds of both cars at the instant she overtakes him.

Kathy Kool buys a sports car that can accelerate at the rate of $4.90 \mathrm{m} / \mathrm{s}^{2} .$ She decides to test the car by racing with another speedster, Stan Speedy. Both start from rest, but experienced Stan leaves the starting line 1.00 s before Kathy. If Stan moves with a constant acceleration of $3.50 \mathrm{m} / \mathrm{s}^{2}$ and Kathy maintains an acceleration of $4.90 \mathrm{m} / \mathrm{s}^{2},$ find.
(a) the time at which Kathy overtakes Stan, (b) the distance she travels before she catches him, and (c) the speeds of both cars at the instant she overtakes him.

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Key Concepts

Uniform Acceleration

Uniform acceleration refers to a motion where the acceleration remains constant throughout the duration of the motion. This concept allows the use of specific kinematic equations, such as s = ut + 1/2at² for displacement and v = u + at for velocity, to analyze and predict various aspects of an object's motion over time.

Kinematic Equations

Kinematic equations are mathematical formulas used to describe the motion of objects under constant acceleration. They relate displacement, initial velocity, acceleration, and time, and are essential tools for solving problems involving uniformly accelerated motion.

Relative Motion

Relative motion involves analyzing the motion of one object in relation to another. This is particularly important when comparing two objects that start at different times or positions, as it provides a framework for determining when and where one object overtakes the other by considering their respective motions.

Time Shift Consideration

Time shift consideration involves accounting for differences in start times when analyzing the motion of multiple objects. This concept is crucial when one object begins moving before or after another, requiring adjustments in the calculations to accurately compare positions and determine points of intersection or overtaking.

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