Assume the cheetah and gazelle run along a straight line. At time t = 0 s the prey, at a certain distance away from the predator, spots the predator and both accelerate to their top speeds starting from rest. a) SET-UP: Draw a diagram showing the initial conditions of the cheetah and gazelle. Label the variables that are known and those that are unknown. b) SOLVE: How far can the cheetah run before it gets exhausted? c) SOLVE: How far can the gazelle run before the cheetah is exhausted?
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.
| Animal | Acceleration | Top speed | Stamina |
| Thomson’s gazelle | 0 – 90 km/h in 18 s | 90 km/h | Can go at top speed for a long time |
| Cheetah | 0 – 120 km/h in 3 s | 120 km/h | Can go at top speed for only 30 s |
Assume the cheetah and gazelle run along a straight line. At time t = 0 s the prey, at a certain distance away from the predator, spots the predator and both accelerate to their top speeds starting from rest.
a) SET-UP: Draw a diagram showing the initial conditions of the cheetah and gazelle. Label the variables that are known and those that are unknown.
b) SOLVE: How far can the cheetah run before it gets exhausted?
c) SOLVE: How far can the gazelle run before the cheetah is exhausted?
d) SOLVE: Based on your answers to (b) and (c) what is the minimum distance away from the cheetah that the gazelle needs to be in order to not get caught?
e) Draw both a position versus time graph and velocity versus time graph of the cheetah and gazelle based on your answers from (b)-(d). You should plot the cheetah and gazelle’s position versus time on a single graph, and similarly for their velocity. Label your axes and their units.
f) REFLECT: Do your answers make sense? are the units of your solution correct? is the magnitude of the solution reasonable? are your graphs consistent with the motion
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