Ann and Carol are driving their cars along the same straight...

Ann and Carol are driving their cars along the same straight road. Carol is located at $x=2.4 \mathrm{mi}$ at $t=0 \mathrm{~h}$ and drives at a steady $36 \mathrm{mph}$. Ann, who is traveling in the same direction, is located at $x=0.0 \mathrm{mi}$ at $t=0.50 \mathrm{~h}$ and drives at a steady $50 \mathrm{mph}$. a. At what time does Ann overtake Carol? b. What is their position at this instant? c. Draw a position-versus-time graph showing the motion of both Ann and Carol.

Ann and Carol are driving their cars along the same straight road. Carol is located at $x=2.4 \mathrm{mi}$ at $t=0 \mathrm{~h}$ and drives at a steady $36 \mathrm{mph}$. Ann, who is traveling in the same direction, is located at $x=0.0 \mathrm{mi}$ at $t=0.50 \mathrm{~h}$ and drives at a steady $50 \mathrm{mph}$.
a. At what time does Ann overtake Carol?
b. What is their position at this instant?
c. Draw a position-versus-time graph showing the motion of both Ann and Carol.

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Key Concepts

Uniform Motion

Uniform motion refers to movement at a constant speed in a straight line. This concept allows the position of a moving object to be described by a linear equation, where the position is determined by its starting point and the product of its speed and time elapsed.

Relative Motion

Relative motion involves analyzing the movement of one object in comparison to another. When considering two objects moving in the same direction, their relative speed (the difference between their speeds) is critical for determining the time and location at which one overtakes the other.

Intersection of Linear Equations

In problems involving overtaking, the positions of two objects moving uniformly can be represented as linear equations. Finding the time or position where one object overtakes the other involves setting these equations equal to each other to determine their intersection point.

Position-Time Graph

A position-time graph is a visual tool where an object's position is plotted against time. In this graph, objects moving with constant speed appear as straight lines, with the slope representing speed. The point where the lines intersect indicates the moment when the positions of the objects coincide.

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