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In a marathon race Chad is out in front, running due north at a speed of 4.00 m/s. John is 95 m behind him, running due north at a speed of 4.50 m/s. How long does it take for John to pass Chad?

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Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

Rutgers, The State University of New Jersey

Simon Fraser University

University of Sheffield

McMaster University

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

10:12

A vector is a mathematical entity that has a magnitude (or length) and direction. The vector is represented by a line segment with a definite beginning, direction, and magnitude. Vectors are added by adding their respective components, and multiplied by a scalar (or a number) to scale the vector.

02:43

In a marathon race Chad is…

0:00

00:59

Two runners approaching ea…

02:31

A man runs at a velocity o…

03:09

Pablo is running in a half…

02:16

In a $5.00 \mathrm{km}$ ra…

03:48

Near the end of a marathon…

01:13

A sprinter runs the 100 yd…

so the question states that two people were running a marathon. One person is running at four meters per second while the other person that's 95 meters away is running at 4.5 meters per second. And we're trying to find when this person passes the person that's running four meters per second. So if we call this the origin say this is where the displacement is. Zero we can use our kingdom attics formulas which state that the velocity times the time, plus some initial displacement is equal to the final displacement. And so, for the person that's running at four meters per second there, velocity is for meters per second times a time with their initial displacement as 95 meters. Because we're saying the origin is where this 4.5 meter per second person is starting to run equal to the final displacement, and for this person that's running 4.5 meters per second. There. Equation, which describes their motion, is just 4.5 tee times at 4.5 times team is equal to the final um, displacement, and so when this person passes, the person that's running four meters per second, Their displacements are gonna be equal. So we can set these two equations equal to each other. And we'll get 4.5 t equals for tea plus 95. We can simplify, and we'll see that 0.5 T equals 95 and solving for tea. We get that T is equal to 190 seconds.

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