At t = 0, one athlete in a race running on a long, straight track with a constant speed υ1 is a distance d1 behind a second athlete running with a constant speed υ2. (a) Under what circumstances is the first athlete able to overtake the second athlete? (b) Find the time t at which the first athlete overtakes the second athlete, in terms of d1, υ1, and υ2. (c) At what minimum distance d2 from the leading athlete must the finish line be located so that the trailing athlete can at least tie for first place? Express d2 in terms of d1, υ1, and υ2 byusing the result of part (b).
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
At t = 0, one athlete in a race running on a long, straight track with a constant speed υ1 is a distance d1 behind a second athlete running with a constant speed υ2. (a) Under what circumstances is the first athlete able to overtake the second athlete? (b) Find the time t at which the first athlete overtakes the second athlete, in terms of d1, υ1, and υ2. (c) At what minimum distance d2 from the leading athlete must the finish line be located so that the trailing athlete can at least tie for first place? Express d2 in terms of d1, υ1, and υ2 by
using the result of part (b).
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