Jenny and Alyssa are members of the cross-country team. On a...

Jenny and Alyssa are members of the cross-country team. On a training run, Jenny starts off and runs at a constant $3.8 \mathrm{m} / \mathrm{s}$. Alyssa starts $15 \mathrm{s}$ later and runs at a constant $4.0 \mathrm{m} / \mathrm{s} .$ At what time after Jenny's start does Alyssa catch up with Jenny?

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Key Concepts

Time Delay Effect

The time delay concept involves scenarios where one mover starts their motion later than another. This delay creates an initial head start in distance for the first mover, and it must be accounted for when determining the time required for the second mover to catch up. Recognizing and correctly incorporating the time delay is key to solving catch-up problems in uniform motion.

Relative Speed

Relative speed is the rate at which the distance between two moving objects changes. In catch-up problems, where one object starts later or moves faster than the other, the difference in their speeds is used to determine how quickly one object can close the gap between them. This is especially useful when comparing the motions of two objects moving in the same direction.

Uniform Motion

This concept refers to the motion of an object at a constant speed in a straight line. In such scenarios, the distance traveled by an object is directly proportional to the time elapsed, and the relationship is expressed as distance = speed × time. This principle is essential for setting up equations to relate the distances covered by different moving objects.

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